Basic Statistics for Business & Economics

Douglas A. Lind, William G.Marchal, Samuel A. Wathen

Chapter 7

Continuous Probability Distributions - all with Video Answers

Educators

Chapter Questions

Problem 1

A uniform distribution is defined over the interval from 6 to 10.
a. What are the values for $a$ and $b$ ?
b. What is the mean of this uniform distribution?
c. What is the standard deviation?
d. Show that the total area is 1.00 .
e. Find the probability of a value more than 7 .
f. Find the probability of a value between 7 and $9 .$

Jon Southam

Jon Southam

Numerade Educator

Problem 2

A uniform distribution is defined over the interval from 2 to $5 .$
a. What are the values for $a$ and $b$ ?
b. What is the mean of this uniform distribution?
c. What is the standard deviation?
d. Show that the total area is 1.00 .
e. Find the probability of a value more than 2.6
f. Find the probability of a value between 2.9 and 3.7 .

Jon Southam

Numerade Educator

Problem 3

The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $\$ 20$ and $\$ 30$ per share. What is the probability that the stock price will be:
a. More than $\$ 27 ?$
b. Less than $\$ 24 ?$

Jon Southam

Numerade Educator

Problem 4

According to the Insurance Institute of America, a family of four spends between $\$ 400$ and $\$ 3,800$ per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.
a. What is the mean amount spent on insurance?
b. What is the standard deviation of the amount spent?
c. If we select a family at random, what is the probability they spend less than $\$ 2,000$ per year on insurance?
d. What is the probability a family spends more than $\$ 3,000$ per year?

Jon Southam

Numerade Educator

Problem 5

The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches.
a. What are the values for $a$ and $b ?$
b. What is the mean amount of rainfall for the month? What is the standard deviation?
c. What is the probability of less than an inch of rain for the month?
d. What is the probability of exactly 1.00 inch of rain?
e. What is the probability of more than 1.50 inches of rain for the month?

Jon Southam

Numerade Educator

Problem 6

Customers experiencing technical difficulty with their Internet cable service may call an 800 number for technical support. It takes the technician between 30 seconds and 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.
a. What are the values for $a$ and $b$ in minutes?
b. What is the mean time to resolve the problem? What is the standard deviation of the time?
c. What percent of the problems take more than 5 minutes to resolve?
d. Suppose we wish to find the middle $50 \%$ of the problem-solving times. What are the end points of these two times?

Jon Southam

Numerade Educator

Problem 7

Explain what is meant by this statement: "There is not just one normal probability distribution but a 'family' of them."

Jon Southam

Numerade Educator

Problem 8

List the major characteristics of a normal probability distribution.

Jon Southam

Numerade Educator

Problem 9

The mean of a normal probability distribution is $500 ;$ the standard deviation is $10 .$
a. About $68 \%$ of the observations lie between what two values?
b. About $95 \%$ of the observations lie between what two values?
c. Practically all of the observations lie between what two values?

Jon Southam

Numerade Educator

Problem 10

The mean of a normal probability distribution is $60 ;$ the standard deviation is 5 .
a. About what percent of the observations lie between 55 and $65 ?$
b. About what percent of the observations lie between 50 and $70 ?$
c. About what percent of the observations lie between 45 and $75 ?$

Nick Johnson

Numerade Educator

Problem 11

The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $\$ 50,000$ per year. Rachel works in the retail industry, where the mean salary for executives with less than 5 years' experience is $\$ 35,000$ with a standard deviation of $\$ 8,000$. Rob is an engineer. The mean salary for engineers with less than 5 years' experience is $\$ 60,000$ with a standard deviation of $\$ 5,000$. Compute the $z$ values for both Rob and Rachel, and comment on your findings.

Jon Southam

Numerade Educator

Problem 12

A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $\$ 90$ with a standard deviation of $\$ 22 .$ Monte's Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $\$ 75,$ and it was $\$ 100$ for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute $z$ values for each, and comment on your findings.

Jon Southam

Numerade Educator

Problem 13

A normal population has a mean of 20.0 and a standard deviation of $4.0 .$
a. Compute the $z$ value associated with 25.0 .
b. What proportion of the population is between 20.0 and $25.0 ?$
c. What proportion of the population is less than $18.0 ?$

Jon Southam

Numerade Educator

Problem 14

A normal population has a mean of 12.2 and a standard deviation of $2.5 .$
a. Compute the $z$ value associated with 14.3 .
b. What proportion of the population is between 12.2 and $14.3 ?$
c. What proportion of the population is less than $10.0 ?$

Jon Southam

Numerade Educator

Problem 15

A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly wage was $\$ 20.50,$ with a standard deviation of $\$ 3.50 .$ Assume the distribution of hourly wages follows the normal probability distribution. If we select a crew member at random, what is the probability the crew member earns:
a. Between $\$ 20.50$ and $\$ 24.00$ per hour?
b. More than $\$ 24.00$ per hour?
c. Less than $\$ 19.00$ per hour?

Jon Southam

Numerade Educator

Problem 16

The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds.
a. What is the area between 415 pounds and the mean of 400 pounds?
b. What is the area between the mean and 395 pounds?
c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

Jon Southam

Numerade Educator

Problem 17

A normal distribution has a mean of 50 and a standard deviation of 4.
a. Compute the probability of a value between 44.0 and 55.0 .
b. Compute the probability of a value greater than 55.0 .
c. Compute the probability of a value between 52.0 and 55.0 .

Jon Southam

Numerade Educator

Problem 18

A normal population has a mean of 80.0 and a standard deviation of $14.0 .$
a. Compute the probability of a value between 75.0 and 90.0 .
b. Compute the probability of a value of 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0 .

Jon Southam

Numerade Educator

Problem 19

Suppose the Internal Revenue Service reported that the mean tax refund for the year 2017 was $\$ 2,800 .$ Assume the standard deviation is $\$ 450$ and that the amounts refunded follow a normal probability distribution.
a. What percent of the refunds are more than $\$ 3,100 ?$
b. What percent of the refunds are more than $\$ 3,100$ but less than $\$ 3,500 ?$
c. What percent of the refunds are more than $\$ 2,250$ but less than $\$ 3,500 ?$

Jon Southam

Numerade Educator

Problem 20

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 29 million and a standard deviation of 5 million. What is the probability next week's show will:
a. Have between 30 and 34 million viewers?
b. Have at least 23 million viewers?
c. Exceed 40 million viewers?

Jon Southam

Numerade Educator

Problem 21

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in for:
a. More than 20 minutes?
b. 20 minutes or less?
c. Between 10 and 12 minutes?

Jon Southam

Numerade Educator

Problem 22

Among the thirty largest U.S. cities, the mean one-way commute time to work is 25.8 minutes. The longest one-way travel time is in New York City, where the mean time is 39.7 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.5 minutes.
a. What percent of the New York City commutes are for less than 30 minutes?
b. What percent are between 30 and 35 minutes?
c. What percent are between 30 and 50 minutes?

Jon Southam

Numerade Educator

Problem 23

A normal distribution has a mean of 50 and a standard deviation of 4 . Determine the value below which $95 \%$ of the observations will occur.

Jon Southam

Numerade Educator

Problem 24

A normal distribution has a mean of 80 and a standard deviation of 14 . Determine the value above which $80 \%$ of the values will occur.

Jon Southam

Numerade Educator

Problem 25

Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $\$ 2,100$ per hour and a standard deviation of $\$ 250 .$ What is the operating cost for the lowest $3 \%$ of the airplanes?

Jon Southam

Numerade Educator

Problem 27

According to media research, the typical American listened to 195 hours of music in the last year. This is down from 290 hours 4 years earlier. Dick Trythal is a big country and western music fan. He listens to music while working around the house, reading, and riding in his truck. Assume the number of hours spent listening to music follows a normal probability distribution with a standard deviation of 8.5 hours.
a. If Dick is in the top $1 \%$ in terms of listening time, how many hours did he listen last year?
b. Assume that the distribution of times 4 years earlier also follows the normal probability distribution with a standard deviation of 8.5 hours. How many hours did the $1 \%$ who listen to the least music actually listen?

Jon Southam

Numerade Educator

Problem 28

For the most recent year available, the mean annual cost to attend a private university in the United States was $\$ 42,224 .$ Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $\$ 4,500 .$ Ninety-five percent of all students at private universities pay less than what amount?

Jon Southam

Numerade Educator

Problem 29

In economic theory, a "hurdle rate" is the minimum return that a person requires before he or she will make an investment. A research report says that annual returns from a specific class of common equities are distributed according to a normal distribution with a mean of $12 \%$ and a standard deviation of $18 \%$. A stock screener would like to identify a hurdle rate such that only 1 in 20 equities is above that value Where should the hurdle rate be set?

Jon Southam

Numerade Educator

Problem 30

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is $12,200 .$ The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. How many pages should the manufacturer advertise for each cartridge if it wants to be correct $99 \%$ of the time?

Jon Southam

Numerade Educator

Problem 31

The amount of cola in a 12 -ounce can is uniformly distributed between 11.96 ounces and 12.05 ounces.
a. What is the mean amount per can?
b. What is the standard deviation amount per can?
c. What is the probability of selecting a can of cola and finding it has less than 12 ounces?
d. What is the probability of selecting a can of cola and finding it has more than 11.98 ounces?
e. What is the probability of selecting a can of cola and finding it has more than 11.00 ounces?

Prashant Bana

Numerade Educator

Problem 32

A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste remaining in the tube follows a uniform distribution. From this information, we can determine the following information about the amount remaining in a toothpaste tube without invading anyone's privacy.
a. How much toothpaste would you expect to be remaining in the tube?
b. What is the standard deviation of the amount remaining in the tube?
c. What is the likelihood there is less than 3.0 ounces remaining in the tube?
d. What is the probability there is more than 1.5 ounces remaining in the tube?

Jon Southam

Numerade Educator

Problem 33

Many retail stores offer their own credit cards. At the time of the credit application, the customer is given a $10 \%$ discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes.
a. What is the mean time for the application process?
b. What is the standard deviation of the process time?
c. What is the likelihood a particular application will take less than 6 minutes?
d. What is the likelihood an application will take more than 5 minutes?

Jon Southam

Numerade Educator

Problem 34

The time patrons at the Grande Dunes Hotel in the Bahamas spend waiting for an elevator follows a uniform distribution between 0 and 3.5 minutes.
a. Show that the area under the curve is 1.00 .
b. How long does the typical patron wait for elevator service?
c. What is the standard deviation of the waiting time?
d. What percent of the patrons wait for less than a minute?
e. What percent of the patrons wait more than 2 minutes?

Jon Southam

Numerade Educator

Problem 35

The net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. Both are normally distributed. For the net sales, the mean is $\$ 180$ million and the standard deviation is $\$ 25$ million. For the number of employees, the mean is 1,500 and the standard deviation is $120 .$ Clarion Fabricators had sales of $\$ 170$ million and 1,850 employees.
a. Convert Clarion's sales and number of employees to $z$ values.
b. Locate the two $z$ values.
c. Compare Clarion's sales and number of employees with those of the other fabricators.

Jon Southam

Numerade Educator

Problem 36

The accounting department at Weston Materials Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.
a. Determine the $z$ values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?
b. What percent of the garages take between 29 hours and 34 hours to erect?
c. What percent of the garages take 28.7 hours or less to erect?
d. Of the garages, $5 \%$ take how many hours or more to erect?

Jon Southam

Numerade Educator

Problem 37

Recently the United States Department of Agriculture issued a report (http://www.cnpp. usda.gov/sites/default/files/CostoffoodMar2015.pdf) indicating a family of four spent an average of about $\$ 890$ per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a standard deviation of $\$ 90$ per month.
a. What percent of the families spend more than $\$ 430$ but less than $\$ 890$ per month on food?
b. What percent of the families spend less than $\$ 830$ per month on food?
c. What percent spend between $\$ 830$ and $\$ 1,000$ per month on food?
d. What percent spend between $\$ 900$ and $\$ 1,000$ per month on food?

Jon Southam

Numerade Educator

Problem 38

A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minute.
a. What is the probability that calls last between 4.2 and 5 minutes?
b. What is the probability that calls last more than 5 minutes?
c. What is the probability that calls last between 5 and 6 minutes?
d. What is the probability that calls last between 4 and 6 minutes?
e. As part of her report to the president, the director of communications would like to report the length of the longest (in duration) $4 \%$ of the calls. What is this time?

Jon Southam

Numerade Educator

Problem 39

Shaver Manufacturing Inc. offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of $\$ 1,280$ and a standard deviation of $\$ 420$ per year.
a. What is the probability that annual dental expenses are more than $\$ 1,500 ?$
b. What is the probability that annual dental expenses are between $\$ 1,500$ and $\$ 2,000 ?$
c. Estimate the probability that an employee had no annual dental expenses.
d. What was the cost for the $10 \%$ of employees who incurred the highest dental expense?

Jon Southam

Numerade Educator

Problem 40

The annual commissions earned by sales representatives of Machine Products Inc., a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $\$ 40,000$ and the standard deviation is $\$ 5,000 .$
a. What percent of the sales representatives earn more than $\$ 42,000$ per year?
b. What percent of the sales representatives earn between $\$ 32,000$ and $\$ 42,000 ?$
c. What percent of the sales representatives earn between $\$ 32,000$ and $\$ 35,000 ?$
d. The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $\$ 1,000$. He can award a bonus to $20 \%$ of the representatives. What is the cutoff point between those who earn a bonus and those who do not?

Jon Southam

Numerade Educator

Problem 41

According to the South Dakota Department of Health, the number of hours of TV viewing per week is higher among adult women than adult men. A recent study showed women spent an average of 34 hours per week watching TV and men, 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men.
a. What percent of the women watch TV less than 40 hours per week?
b. What percent of the men watch TV more than 25 hours per week?
c. How many hours of TV do the $1 \%$ of women who watch the most TV per week watch? Find the comparable value for the men.

Jon Southam

Numerade Educator

Problem 42

According to a government study, among adults in the 25 - to 34 -year age group, the mean amount spent per year on reading and entertainment is $\$ 1,994 .$ Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $\$ 450 .$
a. What percent of the adults spend more than $\$ 2,500$ per year on reading and entertainment?
b. What percent spend between $\$ 2,500$ and $\$ 3,000$ per year on reading and entertainment?
c. What percent spend less than $\$ 1,000$ per year on reading and entertainment?

Jon Southam

Numerade Educator

Problem 43

Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest $5 \%$ of production, based on past experience. Past records indicate weekly production follows the normal distribution. The mean of this distribution is 4,000 units per week and the standard deviation is 60 units per week. If the bonus is paid on the upper $5 \%$ of production, the bonus will be paid on how many units or more?

Sheryl Ezze

Numerade Educator

Problem 44

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation was 2,000 miles.
a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more?
b. What percent of the trucks logged more than 57,060 but less than 58,280 miles?
c. What percent of the Fords traveled 62,000 miles or less during the year?
d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain.

Jon Southam

Numerade Educator

Problem 45

Best Electronics Inc. offers a "no hassle" returns policy. The daily number of customers returning items follows the normal distribution. The mean number of customers returning items is 10.3 per day and the standard deviation is 2.25 per day.
a. For any day, what is the probability that eight or fewer customers returned items?
b. For any day, what is the probability that the number of customers returning items is between 12 and $14 ?$
c. Is there any chance of a day with no customer returns?

Jon Southam

Numerade Educator

Problem 46

The funds dispensed at the ATM machine located near the checkout line at the Kroger's in Union, Kentucky, follows a normal probability distribution with a mean of $\$ 4,200$ per day and a standard deviation of $\$ 720$ per day. The machine is programmed to notify the nearby bank if the amount dispensed is very low (less than $\$ 2,500$ ) or very high (more than $\$ 6,000$ ).
a. What percent of the days will the bank be notified because the amount dispensed is very low?
b. What percent of the time will the bank be notified because the amount dispensed is high?
c. What percent of the time will the bank not be notified regarding the amount of funds dispersed?

Jon Southam

Numerade Educator

Problem 47

The weights of canned hams processed at Henline Ham Company follow the normal distribution, with a mean of 9.20 pounds and a standard deviation of 0.25 pound. The label weight is given as 9.00 pounds.
a. What proportion of the hams actually weigh less than the amount claimed on the label?
b. The owner, Glen Henline, is considering two proposals to reduce the proportion of hams below label weight. He can increase the mean weight to 9.25 and leave the standard deviation the same, or he can leave the mean weight at 9.20 and reduce the standard deviation from 0.25 pound to $0.15 .$ Which change would you recommend?

Jon Southam

Numerade Educator

Problem 48

A recent Gallup study (http://www.gallup.com/poll/175286/hour-workweek-actually-Ionger-seven-hours.aspx?g_source=polls+work+hours$\&$g_medium=search$\&$g_campaign=tiles)
found the typical American works an average of 46.7 hour per week. The study did not report the shape of the distribution of hours worked or the standard deviation. It did, however, indicate that $40 \%$ of the workers worked less than 40 hours a week and that 18 percent worked more than 60 hours.
a. If we assume that the distribution of hours worked is normally distributed, and knowing $40 \%$ of the workers worked less than 40 hours, find the standard deviation of the distribution.
b. If we assume that the distribution of hours worked is normally distributed and $18 \%$ of the workers worked more than 60 hours, find the standard deviation of the distribution.
c. Compare the standard deviations computed in parts $a$ and $b$. Is the assumption that the distribution of hours worked is approximately normal reasonable? Why?

Jon Southam

Numerade Educator

Problem 49

Most four-year automobile leases allow up to 60,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follows the normal distribution. The mean is 52,000 miles and the standard deviation is 5,000 miles.
a. What percent of the leases will yield a penalty because of excess mileage?
b. If the automobile company wanted to change the terms of the lease so that $25 \%$ of the leases went over the limit, where should the new upper limit be set?
c. One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?

Jon Southam

Numerade Educator

Problem 50

The price of shares of Bank of Florida at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $\$ 42.00$ per share and the standard deviation was $\$ 2.25$ per share.
a. What is the probability that the end-of-day trading price is over $\$ 45.00 ?$ Estimate the number of days in a year when the trading price finished above $\$ 45.00 .$
b. What percent of the days was the price between $\$ 38.00$ and $\$ 40.00 ?$
c. What is the minimum share price for the top $15 \%$ of end-of-day trading prices?

Jon Southam

Numerade Educator

Problem 51

The annual sales of romance novels follow the normal distribution. However, the mean and the standard deviation are unknown. Forty percent of the time, sales are more than $470,000,$ and $10 \%$ of the time, sales are more than $500,000 .$ What are the mean and the standard deviation?

Jon Southam

Numerade Educator

Problem 52

In establishing warranties on HDTVs, the manufacturer wants to set the limits so that few will need repair at the manufacturer's expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV, the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only $10 \%$ of the HDTVs need repairs at the manufacturer's expense?

Jon Southam

Numerade Educator

Problem 53

Refer to the North Valley Real Estate data, which report information on homes sold during the last year.
a. The mean selling price (in $\$$ thousands) of the homes was computed earlier to be $\$ 357.0$, with a standard deviation of $\$ 160.7$. Use the normal distribution to estimate the percentage of homes selling for more than $\$ 500,000$. Compare this to the actual results. Is price normally distributed? Try another test. If price is normally distributed, how many homes should have a price greater than the mean? Compare this to the actual number of homes. Construct a frequency distribution of price. What do you observe?
b. The mean days on the market is 30 with a standard deviation of 10 days. Use the normal distribution to estimate the number of homes on the market more than 24 days. Compare this to the actual results. Try another test. If days on the market is normally distributed, how many homes should be on the market more than the mean number of days? Compare this to the actual number of homes. Does the normal distribution yield a good approximation of the actual results? Create a frequency distribution of days on the market. What do you observe?

Jon Southam

Numerade Educator

Problem 54

Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season.
a. The mean attendance per team for the season was 2.439 million, with a standard deviation of 0.618 million. Use the normal distribution to estimate the number of teams with attendance of more than 3.5 million. Compare that estimate with the actual number. Comment on the accuracy of your estimate.
b. The mean team salary was $\$ 121$ million, with a standard deviation of $\$ 40.0$ million. Use the normal distribution to estimate the number of teams with a team salary of more than $\$ 100$ million. Compare that estimate with the actual number. Comment on the accuracy of the estimate.

Jon Southam

Numerade Educator

Problem 55

Refer to the Lincolnville School District bus data.
a. Refer to the maintenance cost variable. The mean maintenance cost for last year is $\$ 4,552$ with a standard deviation of $\$ 2332 .$ Estimate the number of buses with a maintenance cost of more than $\$ 6,000$. Compare that with the actual number. Create a frequency distribution of maintenance cost. Is the distribution normally distributed?
b. Refer to the variable on the number of miles driven since the last maintenance. The mean is 11,121 and the standard deviation is 617 miles. Estimate the number of buses traveling more than 11,500 miles since the last maintenance. Compare that number with the actual value. Create a frequency distribution of miles since maintenance cost. Is the distribution normally distributed?

Jon Southam

Numerade Educator