Question

8. The number of minutes needed to finish the Probability Distributions Unit Test is Normally distributed with a mean of 70 minutes and a standard deviation of 10 minutes. a. What proportion of students will finish the test in less than 55 minutes? b. What proportion of students will take between 48 and 72 minutes to finish the test? c. What proportion of students will take longer than 68 minutes to finish the test? 9. Mackenzie stops for coffee every day on her way to school and it often makes her late. The number of minutes Mackenzie is late is Normally distributed with a mean of 15 minutes and a standard deviation of 7 minutes. a. What percent of the time is Mackenzie more than 20 minutes late to school? b. What percent of the time is Mackenzie on time to school? 10. A survey asks students how long it takes to drive to school, park the car, and get to their first period class. After analyzing the data, it is determined that the data is Normally distributed with a mean of 12 minutes and a standard deviation of 3 minutes. a. Juan's travel time is 14 minutes; determine his z-score. b. Elizabeth's z-score is -1.45. Interpret her z-score and find her travel time. 11. Determine whether the underlined value is a parameter or a statistic; explain your reasoning. a. The mean height of an NBA basketball player is 79 inches. b. In the 2016 Presidential election, only 56% of registered voters actually voted. c. The average weight of an SRS of 12 6-month old Springer Spaniel puppies was 8.2 lbs. 12. Male Beluga whales have a mean weight of 1980 pounds with a standard deviation of 220 pounds. Assume that weights are Normally distributed. a. Sketch and label the Normal curve. b. Find the probability that a randomly selected Beluga whale weighs between 1900 and 2100 pounds. c. Find the probability that an SRS of 10 Belugas has a mean weight between 1900 and 2100 pounds. 13. According to the Center for Disease Control, only 58.8% of high school students always wore seat belts when riding as passengers. Suppose that a survey contacts an SRS of 100 high school seniors and calculates the sample proportion, p? , in this sample who always wear seat belts when riding as passengers. a. What is the mean and standard deviation of the sampling distribution of p? ? b. What is the probability, in an SRS of 100 high school seniors, that between 55% and 60% of them always wear seat belts when riding as passengers? c. If the sample size were 400 rather than 100, how would this change the curve of the sampling distribution p??

9. Mackenzie stops for coffee every day on her way to school and it often makes her late. The number of minutes Mackenzie is late is Normally distributed with a mean of 15 minutes and a standard deviation of 7 minutes.
a. What percent of the time is Mackenzie more than 20 minutes late to school?
b. What percent of the time is Mackenzie on time to school?

10. A survey asks students how long it takes to drive to school, park the car, and get to their first period class. After analyzing the data, it is determined that the data is Normally distributed with a mean of 12 minutes and a standard deviation of 3 minutes.
a. Juan's travel time is 14 minutes; determine his z-score.
b. Elizabeth's z-score is -1.45. Interpret her z-score and find her travel time.

11. Determine whether the underlined value is a parameter or a statistic; explain your reasoning.
a. The mean height of an NBA basketball player is 79 inches.
b. In the 2016 Presidential election, only 56% of registered voters actually voted.
c. The average weight of an SRS of 12 6-month old Springer Spaniel puppies was 8.2 lbs.

12. Male Beluga whales have a mean weight of 1980 pounds with a standard deviation of 220 pounds. Assume that weights are Normally distributed.
a. Sketch and label the Normal curve.
b. Find the probability that a randomly selected Beluga whale weighs between 1900 and 2100 pounds.
c. Find the probability that an SRS of 10 Belugas has a mean weight between 1900 and 2100 pounds.

13. According to the Center for Disease Control, only 58.8% of high school students always wore seat belts when riding as passengers. Suppose that a survey contacts an SRS of 100 high school seniors and calculates the sample proportion, p? , in this sample who always wear seat belts when riding as passengers.
a. What is the mean and standard deviation of the sampling distribution of p? ?
b. What is the probability, in an SRS of 100 high school seniors, that between 55% and 60% of them always wear seat belts when riding as passengers?
c. If the sample size were 400 rather than 100, how would this change the curve of the sampling distribution p??

8. The number of minutes needed to finish the Probability Distributions Unit Test is Normally distributed with a mean of 70 minutes and a standard deviation of 10 minutes.
a. What proportion of students will finish the test in less than 55 minutes?
b. What proportion of students will take between 48 and 72 minutes to finish the test?
c. What proportion of students will take longer than 68 minutes to finish the test?

9. Mackenzie stops for coffee every day on her way to school and it often makes her late. The number of minutes Mackenzie is late is Normally distributed with a mean of 15 minutes and a standard deviation of 7 minutes.
a. What percent of the time is Mackenzie more than 20 minutes late to school?
b. What percent of the time is Mackenzie on time to school?

10. A survey asks students how long it takes to drive to school, park the car, and get to their first period class. After analyzing the data, it is determined that the data is Normally distributed with a mean of 12 minutes and a standard deviation of 3 minutes.
a. Juan's travel time is 14 minutes; determine his z-score.
b. Elizabeth's z-score is -1.45. Interpret her z-score and find her travel time.

11. Determine whether the underlined value is a parameter or a statistic; explain your reasoning.
a. The mean height of an NBA basketball player is 79 inches.
b. In the 2016 Presidential election, only 56% of registered voters actually voted.
c. The average weight of an SRS of 12 6-month old Springer Spaniel puppies was 8.2 lbs.

12. Male Beluga whales have a mean weight of 1980 pounds with a standard deviation of 220 pounds. Assume that weights are Normally distributed.
a. Sketch and label the Normal curve.
b. Find the probability that a randomly selected Beluga whale weighs between 1900 and 2100 pounds.
c. Find the probability that an SRS of 10 Belugas has a mean weight between 1900 and 2100 pounds.

13. According to the Center for Disease Control, only 58.8% of high school students always wore seat belts when riding as passengers. Suppose that a survey contacts an SRS of 100 high school seniors and calculates the sample proportion, p? , in this sample who always wear seat belts when riding as passengers.
a. What is the mean and standard deviation of the sampling distribution of p? ?
b. What is the probability, in an SRS of 100 high school seniors, that between 55% and 60% of them always wear seat belts when riding as passengers?
c. If the sample size were 400 rather than 100, how would this change the curve of the sampling distribution p??

Added by Elizabeth L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kari Hasz

01/26/2023

Step 1

To find the proportion of students who will finish the test in less than 55 minutes, we need to calculate the z-score for 55 minutes. The z-score is calculated as (X - μ) / σ, where X is the value we're interested in, μ is the mean, and σ is the standard Show more…

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8. The number of minutes needed to finish the Probability Distributions Unit Test is Normally distributed with a mean of 70 minutes and a standard deviation of 10 minutes. a. What proportion of students will finish the test in less than 55 minutes? b. What proportion of students will take between 48 and 72 minutes to finish the test? c. What proportion of students will take longer than 68 minutes to finish the test? 9. Mackenzie stops for coffee every day on her way to school and it often makes her late. The number of minutes Mackenzie is late is Normally distributed with a mean of 15 minutes and a standard deviation of 7 minutes. a. What percent of the time is Mackenzie more than 20 minutes late to school? b. What percent of the time is Mackenzie on time to school? 10. A survey asks students how long it takes to drive to school, park the car, and get to their first period class. After analyzing the data, it is determined that the data is Normally distributed with a mean of 12 minutes and a standard deviation of 3 minutes. a. Juan's travel time is 14 minutes; determine his z-score. b. Elizabeth's z-score is -1.45. Interpret her z-score and find her travel time. 11. Determine whether the underlined value is a parameter or a statistic; explain your reasoning. a. The mean height of an NBA basketball player is 79 inches. b. In the 2016 Presidential election, only 56% of registered voters actually voted. c. The average weight of an SRS of 12 6-month old Springer Spaniel puppies was 8.2 lbs. 12. Male Beluga whales have a mean weight of 1980 pounds with a standard deviation of 220 pounds. Assume that weights are Normally distributed. a. Sketch and label the Normal curve. b. Find the probability that a randomly selected Beluga whale weighs between 1900 and 2100 pounds. c. Find the probability that an SRS of 10 Belugas has a mean weight between 1900 and 2100 pounds. 13. According to the Center for Disease Control, only 58.8% of high school students always wore seat belts when riding as passengers. Suppose that a survey contacts an SRS of 100 high school seniors and calculates the sample proportion, p̂ , in this sample who always wear seat belts when riding as passengers. a. What is the mean and standard deviation of the sampling distribution of p̂ ? b. What is the probability, in an SRS of 100 high school seniors, that between 55% and 60% of them always wear seat belts when riding as passengers? c. If the sample size were 400 rather than 100, how would this change the curve of the sampling distribution p̂?

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00:02 We have a mean of 70 and a standard deviation of 10.

00:08 We're going to find the probability that x is less than 55, the probability that x is between 48 and 72, and the probability that x is greater than 68.

00:23 So we'll take the probability that z is less than 55 minus 70 divided by 10, which gives us a z score of negative 1 .5, which has a probability of 0 .0668.

00:37 Here we'll do 48 minus 70 divided by 10 is less than z, which is less than 72 minus 70 divided by 10.

00:46 That's going to put z in between negative 2 .2 and 0 .2, which means we're going to take 0 .5793 and subtract 0 .039 to get our probability of 0 .5609 to get our probability of 0 .560.

01:04 654.

01:08 Oops, i'm running out of space here.

01:10 There we go.

01:11 Four.

01:14 Okay.

01:15 For part c, we'll do 1 minus the probability that z is less than 68 minus 70 divided by 10.

01:22 That's going to give us one minus the probability that z is less than negative 0 .2, which is a probability of 0 .5793.

01:32 For 9, our mean is 15, and our standard deviation is 7.

01:38 And we're going to find the percent of time that a person is more than 20 minutes late to school.

01:45 So the probability that x is greater than 20 means that we're going to do one minus the probability that z is less than 20 minus 15 divided by 7.

01:55 So that's one minus the probability that z is less than .71, which gives us 0 .2389.

02:01 For part b, if we want to know the percent of time that a person is on time, that means they are zero minutes late or less.

02:12 So the probability that z is less than 0 minus 15 divided by 7 is the probability that z is less than negative 2 .14, which is 0 .162.

02:25 For number 10, we have a mean of 12, so a mean of 12, and a standard deviation of 3.

02:36 Wands travel time is 14 minutes to determine the z score.

02:39 So z would be 14 minus 12 divided by 3, and that would be 0 .67.

02:50 If we have a z score of negative 1 .45, what would the travel time be? so we would take x bar minus 12 divided by 13 and solve it for x bar.

03:01 And when we do that, we're going to get 7 .65.

03:08 Number 11.

03:10 Determine whether the underlying value is a parameter or a statistic and explain your reasoning.

03:16 The mean height of an nba basketball player is 79 inches.

03:21 This would be a parameter because it represents the population of nba basketball players.

03:29 In 2016 presidential election, only 56 % of registered voters actually voted.

03:36 Again, if we're looking at the population of registered voters, this is also going to be a parameter.

03:45 Part c, the average weight of an srs of 12, 6 -month -old springer spaniel puppies was 8 .2.

03:51 Well, srs stands for a simple random sample, so that makes this a statistic...

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