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In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 36 mpg and a standard deviation of 1.6 mpg. Suppose that the car manufacturer samples seven cars from its assembly line and tests them for mileage ratings. a. What is the distribution of the mean mpg for the sample? b. What is the probability that the mean mpg of the sample will be greater than 37 mpg? c. What is the probability that the mean mpg of the sample will be less than 35.5 mpg? a. What is the distribution of the mean mpg for the sample? Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to two decimal places as needed.) O A. The sampling distribution of the mean follows an exponential distribution with the sample mean the standard deviation of the sample mean mpg. B. The sampling distribution of the mean follows a uniform distribution with the sample mean standard deviation of the sample mean mpg. O C. The sampling distribution of the mean follows a triangular distribution with the sample mean standard deviation of the sample mean mpg. mean D. The sampling distribution of the mean follows a normal distribution with the sample mea standard deviation of the sample mean mpg. b. The probability that the mean mpg of the sample will be greater than 37 mpg is (Round to four decimal places as needed.) c. The probability that the mean mpg of the sample will be less than 35.5 mpg is (Round to four decimal places as needed.) mpg and mpg and the mpg and the mpg and the

In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 36 mpg and a standard deviation of 1.6 mpg. Suppose that the car manufacturer samples seven cars from its assembly line and tests them for mileage ratings. a. What is the distribution of the mean mpg for the sample? b. What is the probability that the mean mpg of the sample will be greater than 37 mpg? c. What is the probability that the mean mpg of the sample will be less than 35.5 mpg? a. What is the distribution of the mean mpg for the sample? Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to two decimal places as needed.) O A. The sampling distribution of the mean follows an exponential distribution with the sample mean the standard deviation of the sample mean mpg. B. The sampling distribution of the mean follows a uniform distribution with the sample mean standard deviation of the sample mean mpg. O C. The sampling distribution of the mean follows a triangular distribution with the sample mean standard deviation of the sample mean mpg. mean D. The sampling distribution of the mean follows a normal distribution with the sample mea standard deviation of the sample mean mpg. b. The probability that the mean mpg of the sample will be greater than 37 mpg is (Round to four decimal places as needed.) c. The probability that the mean mpg of the sample will be less than 35.5 mpg is (Round to four decimal places as needed.) mpg and mpg and the mpg and the mpg and the

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Educational Text: Understanding Sampling Distributions and Probabilities** In determining automobile mileage ratings, it was found that the miles per gallon (mpg) in the city for a certain model is normally distributed, with a mean of 36 mpg and a standard deviation of 1.6 mpg. Suppose that the car manufacturer samples seven cars from its assembly line and tests them for mileage ratings. **Questions:** a. What is the distribution of the mean mpg for the sample? b. What is the probability that the mean mpg of the sample will be greater than 37 mpg? c. What is the probability that the mean mpg of the sample will be less than 35.5 mpg? --- **Analysis and Solution Steps:** **a. Identify the Distribution:** What is the distribution of the mean mpg for the sample? Choose the correct option and fill in the blanks: - Type integers or decimals rounded to two decimal places as needed. Options: A. The sampling distribution of the mean follows an exponential distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. B. The sampling distribution of the mean follows a uniform distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. C. The sampling distribution of the mean follows a triangular distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. D. The sampling distribution of the mean follows a normal distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. **b. Calculate Probability for Greater than 37 mpg:** The probability that the mean mpg of the sample will be greater than 37 mpg is ___. - Round to four decimal places as needed. **c. Calculate Probability for Less than 35.5 mpg:** The probability that the mean mpg of the sample will be less than 35.5 mpg is ___. - Round to four decimal places as needed. This exercise requires understanding of normal distributions, standard deviations, and how sample sizes affect the sampling distribution.
Transcribed Image Text:**Educational Text: Understanding Sampling Distributions and Probabilities** In determining automobile mileage ratings, it was found that the miles per gallon (mpg) in the city for a certain model is normally distributed, with a mean of 36 mpg and a standard deviation of 1.6 mpg. Suppose that the car manufacturer samples seven cars from its assembly line and tests them for mileage ratings. **Questions:** a. What is the distribution of the mean mpg for the sample? b. What is the probability that the mean mpg of the sample will be greater than 37 mpg? c. What is the probability that the mean mpg of the sample will be less than 35.5 mpg? --- **Analysis and Solution Steps:** **a. Identify the Distribution:** What is the distribution of the mean mpg for the sample? Choose the correct option and fill in the blanks: - Type integers or decimals rounded to two decimal places as needed. Options: A. The sampling distribution of the mean follows an exponential distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. B. The sampling distribution of the mean follows a uniform distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. C. The sampling distribution of the mean follows a triangular distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. D. The sampling distribution of the mean follows a normal distribution with the sample mean ___ mpg and the standard deviation of the sample mean ___ mpg. **b. Calculate Probability for Greater than 37 mpg:** The probability that the mean mpg of the sample will be greater than 37 mpg is ___. - Round to four decimal places as needed. **c. Calculate Probability for Less than 35.5 mpg:** The probability that the mean mpg of the sample will be less than 35.5 mpg is ___. - Round to four decimal places as needed. This exercise requires understanding of normal distributions, standard deviations, and how sample sizes affect the sampling distribution.
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