CNNBC recently reported that the mean annual cost of auto insurance is 956 dollars. Assume the standard deviation is 280 dollars, and the cost is normally distributed. You take a simple random sample of 38 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N( 956 280 b. What is the distribution of ? T - N( 956 c. What is the probability that one randomly selected auto insurance is more than $906? 45.4220 0.5709 d. a simple random sample of 38 auto insurance policies, find the probability that the average cost is more than $906. e. For part d), is the assumption of normal necessary? Yes No o

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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CNNBC recently reported that the mean annual cost of auto insurance is 956 dollars. Assume the standard
deviation is 280 dollars, and the cost is normally distributed. You take a simple random sample of 38 auto
insurance policies. Round your answers to 4 decimal places.
a. What is the distribution of X? X - N( 956
280
b. What is the distribution of ? T - N( 956
c. What is the probability that one randomly selected auto insurance is more than $906?
45.4220
0.5709
d. a simple random sample of 38 auto insurance policies, find the probability that the average cost is
more than $906.
e. For part d), is the assumption of normal necessary?
Yes
No o
Transcribed Image Text:CNNBC recently reported that the mean annual cost of auto insurance is 956 dollars. Assume the standard deviation is 280 dollars, and the cost is normally distributed. You take a simple random sample of 38 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N( 956 280 b. What is the distribution of ? T - N( 956 c. What is the probability that one randomly selected auto insurance is more than $906? 45.4220 0.5709 d. a simple random sample of 38 auto insurance policies, find the probability that the average cost is more than $906. e. For part d), is the assumption of normal necessary? Yes No o
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