Question 6. Question : The Intelligence Quotient (IQ) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103?
Student Answer: 0.3264 0.9428 0.4702 0.7471 Instructor Explanation: We use the formula: ; and . Then, using the "areas under the normal curve" table, P(−0.94 ≤z≤ 1.41) = .3264 + .4207 = .7471.
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Question 7. Question : The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?

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Question 8. Question : The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose we select a sample of 40 tires and use a simulator to determine the tread life. What is the standard error of the mean?
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Question 9. Question : As the size of the sample increases, what happens to the shape of the distribution of sample means?