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# Elementary Statistics 11th

## Educators  ### Problem 43

Demonstrates that probability is equal to area under a curve. Given that college students sleep an average of 7 hours per night, with a standard deviation equal to 1.7 hours, use the scroll bar in the applet to find:
a. $\quad P(\text { a student sleeps between } 5 \text { and } 9$ hours)
b. $\quad P(\text { a student sleeps between } 2 \text { and } 4$ hours)
c. $\quad P(\text { a student sleeps between } 8 \text { and } 11$ hours) Gus S.

### Problem 44

Demonstrates the effects that the mean and standard deviation have on a normal curve.
a. Leaving the standard deviation at $1,$ increase the mean to $3 .$ What happens to the curve?
b. $\quad$ Reset the mean to 0 and increase the standard deviation to $2 .$ What happens to the curve?
c. If you could decrease the standard deviation to 0.5 what do you think would happen to the normal curve? Gus S.

### Problem 45

Given $x=58, \mu=43$ and $\sigma=5.2,$ find $z$ Gus S.

### Problem 46

Given $x=237, \mu=220$ and $\sigma=12.3,$ find $z$. Gus S.

### Problem 47

Given that $x$ is a normally distributed random variable with a mean of 60 and a standard deviation of 10 find the following probabilities.
a. $\quad P(x>60)$
b. $\quad P(60< x<72)$
c. $\quad P(57< x<83)$
d. $\quad P(65< x<82)$
e. $\quad P(38< x<78)$
f. $\quad P(x<38)$ Evelyn C.

### Problem 48

Given that $x$ is a normally distributed random variable with a mean of 28 and a standard deviation of $7,$ find the following probabilities.
a. $\quad P(x<28)$
b. $\quad P(28<x<38)$
c. $\quad P(24<x<40)$
d. $\quad P(30<x<45)$
e. $\quad P(19<x<35)$
f. $\quad P(x<48)$ Evelyn C.

### Problem 49

As shown in Example $6.8,$ IQ scores are considered normally distributed, with a mean of 100 and a standard deviation of 16.
a. Find the probability that a randomly selected person will have an IQ score between 100 and $120 .$
b. Find the probability that a randomly selected person will have an IQ score above $80 .$ Gus S.

### Problem 50

Based on a survey conducted by Greenfield Online, 25 to 34-year-olds spend the most each week on fast food. The average weekly amount of $\$ 44$was reported in a May 2009 USA Today Snapshot. Assuming that weekly fast food expenditures are normally distributed with a standard deviation of$\$14.50,$ what is the probability that a 25- to 34-year-old will spend:
a. less than $\$ 25$a week on fast food? b. between$\$30$ and $\$ 50$a week on fast food? c. more than$\$75$ a week on fast food? Gus S.

### Problem 51

Depending on where you live and on the quality of the day care, costs of day care can range from $\$ 3000$to$\$15,000$ a year (or $\$ 250$to$\$1250$ a month) for one child, according to the Baby Center. Day care centers in large cities such as New York and San Francisco are notoriously expensive. Suppose that day care costs are normally distributed with a mean equal to $\$ 9000$and a standard deviation equal to$\$1800 .$
a. What percentage of day care centers cost between $\$ 7200$and$\$10,800 ?$
b. What percentage of day care centers cost between $\$ 5400$and$\$12,600 ?$
c. What percentage of day care centers cost between $\$ 3600$and$\$14,400 ?$
d. Compare the results in a through c with the empirical rule. Explain the relationship. Evelyn C.

### Problem 52

6.52 According to Collegeboard.com [http://www.collegeboard.com/ $]$ the national average salary for a plumber as of 2007 is $\$ 47,350 .$If we assume that the annual salaries for plumbers are normally distributed with a standard deviation of$\$5250,$ find the following:
a. What percentage earn below $\$ 30,000 ?$b. What percentage earn above$\$63,000 ?$ Gus S.

### Problem 53

According to the Federal Highway Administration's 2006 highway statistics, the distribution of ages for licensed drivers has a mean of 47.5 years and a standard deviation of 16.6 years [www.fhwa.dot.gov]. Assuming the distribution of ages is normally distributed, what percentage of the drivers are:
a. between the ages of 17 and $22 ?$
b. younger than 25 years of age?
c. older than 21 years of age?
d. between the ages of 48 and $68 ?$
e. older than 75 years of age? Evelyn C.

### Problem 54

There is a new working class with money to burn, according to the USA Today March 1, 2005, article "New "gold-collar' young workers gain clout." "Gold-collar" is a subset of blue-collar workers, defined by researchers as those working in fast food and retail jobs, or as security guards, office workers, or hairdressers. These 18- to 25-yearold "gold-collar" workers are spending an average of $\$ 729$a month on themselves (versus$\$267$ for college students and $\$ 609$for blue-collar workers). Assuming this spending is normally distributed with a standard deviation of$\$92.00$ what percentage of gold-collar workers spend:
a. between $\$ 600$and$\$900$ a month on themselves?
b. between $\$ 400$and$\$1000$ a month on themselves?
c. more than $\$ 1050$a month on themselves? d. less than$\$500$ a month on themselves? Evelyn C.

### Problem 55

Findings from a survey of American adults conducted by Yankelovich Partners for the International Bottled Water Association indicate that Americans on the average drink 6.18-ounce servings of water a day [http://www.pangaeawater.com/]. Assuming that the number of 8-ounce servings of water is approximately normally distributed with a standard deviation of 1.4 servings, what proportion of Americans drink
a. more than the recommended 8 servings?
b. less than half the recommended 8 servings? Gus S.
As shown in Example $6.12,$ incomes of junior executives are normally distributed with a standard deviation of $\$ 3828.$a. What is the mean for the salaries of junior executives, if a salary of$\$62,900$ is at the top end of the middle $80 \%$ of incomes?