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The mean number of items purchased by shoppers at a grocery store is strongly skewed right with a mean 14.5 and a standard deviation of 8.6. A random sample of size 100 will be selected. What is the mean and standard deviation of the number of items purchased by shoppers in all possible samples of that size?

The mean number of items purchased by shoppers at a grocery store is strongly skewed right with a mean 14.5 and a standard deviation of 8.6. A random sample of size 100 will be selected. What is the mean and standard deviation of the number of items purchased by shoppers in all possible samples of that size?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The problem appears to be an exercise from a statistics or probability course. Here's the transcription and explanation: --- **Name:** **ID #:** 9. The principal at a local high school asked 100 randomly selected students how many minutes they spend doing homework on a typical school day. The mean of the sample is 72.5 minutes with a standard deviation of 10.8 minutes. Assuming that the distribution of the number of minutes spent on homework is approximately normal, what is the probability that a randomly selected student spends more than 90 minutes on homework? a. 0.1075 b. 0.1335 c. 0.1985 d. 0.2177 e. 0.2843 10. A manufacturer claims that only 2% of the tires produced are defective. A store receives a delivery of 100 tires from the manufacturer. Let \( X \) be the proportion of defective tires in a sample of 100 items. Assuming the conditions for constructing a confidence interval for a proportion are met, what are the mean and standard deviation of the sampling distribution of \( X \)? a. The mean is 0.6 and the standard deviation is 0.28 b. The mean is 6.0 and the standard deviation is 2.53 c. The mean is 0.02 and the standard deviation is 0.014 d. The mean is 0.02 and the standard deviation is 0.196 **Essay** 11. The mean number of items purchased by shoppers at a grocery store is strongly skewed right with a mean of 14.5 and a standard deviation of 6.8. A random sample of size \( n = 100 \) is selected. What is the mean and standard deviation of the number of items purchased by shoppers in all possible samples of this size? 12. The distribution of the age of the employees at a large manufacturing plant is strongly skewed left with a mean of 42.9 years old and a standard deviation of 9.86 years old. What is the approximate probability that the mean age for a sample of size \( n = 35 \) is no more than 40 years old? Explain. a. What is the shape of the sampling distribution of \( \bar{x} \), the sample mean age of the employees for samples of size \( n = 35 \)? b. What
Transcribed Image Text:The problem appears to be an exercise from a statistics or probability course. Here's the transcription and explanation: --- **Name:** **ID #:** 9. The principal at a local high school asked 100 randomly selected students how many minutes they spend doing homework on a typical school day. The mean of the sample is 72.5 minutes with a standard deviation of 10.8 minutes. Assuming that the distribution of the number of minutes spent on homework is approximately normal, what is the probability that a randomly selected student spends more than 90 minutes on homework? a. 0.1075 b. 0.1335 c. 0.1985 d. 0.2177 e. 0.2843 10. A manufacturer claims that only 2% of the tires produced are defective. A store receives a delivery of 100 tires from the manufacturer. Let \( X \) be the proportion of defective tires in a sample of 100 items. Assuming the conditions for constructing a confidence interval for a proportion are met, what are the mean and standard deviation of the sampling distribution of \( X \)? a. The mean is 0.6 and the standard deviation is 0.28 b. The mean is 6.0 and the standard deviation is 2.53 c. The mean is 0.02 and the standard deviation is 0.014 d. The mean is 0.02 and the standard deviation is 0.196 **Essay** 11. The mean number of items purchased by shoppers at a grocery store is strongly skewed right with a mean of 14.5 and a standard deviation of 6.8. A random sample of size \( n = 100 \) is selected. What is the mean and standard deviation of the number of items purchased by shoppers in all possible samples of this size? 12. The distribution of the age of the employees at a large manufacturing plant is strongly skewed left with a mean of 42.9 years old and a standard deviation of 9.86 years old. What is the approximate probability that the mean age for a sample of size \( n = 35 \) is no more than 40 years old? Explain. a. What is the shape of the sampling distribution of \( \bar{x} \), the sample mean age of the employees for samples of size \( n = 35 \)? b. What
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