CNNBC recently reported that the mean annual cost of auto insurance is 968 dollars. Assume the standard deviation is 259 dollars, and the cost is normally distributed. You take a simple random sample of 36 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N b. What is the distribution of ? T - N( c. What is the probability that one randomly selected auto insurance is less than $1015? d. a simple random sample of 36 auto insurance policies, find the probability that the average cost is less than $1015. e. For part d), is the assumption of normal necessary? O YesO No

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CNNBC recently reported that the mean annual cost of auto insurance is 968 dollars. Assume the standard
deviation is 259 dollars, and the cost is normally distributed. You take a simple random sample of 36 auto
insurance policies. Round your answers to 4 decimal places.
a. What is the distribution of X? X - N(
b. What is the distribution of ? T - N(
c. What is the probability that one randomly selected auto insurance is less than $1015?
d. a simple random sample of 36 auto insurance policies, find the probability that the average cost is
less than $1015.
e. For part d), is the assumption of normal necessary? O YesO No
Transcribed Image Text:CNNBC recently reported that the mean annual cost of auto insurance is 968 dollars. Assume the standard deviation is 259 dollars, and the cost is normally distributed. You take a simple random sample of 36 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N( b. What is the distribution of ? T - N( c. What is the probability that one randomly selected auto insurance is less than $1015? d. a simple random sample of 36 auto insurance policies, find the probability that the average cost is less than $1015. e. For part d), is the assumption of normal necessary? O YesO No
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