CNNBC recently reported that the mean annual cost of auto insurance is 979 dollars. Assume the standard deviation is 261 dollars, and the cost is normally distributed. You take a simple random sample of 40 auto insurance policies. Round your answers to 4 decimal places.What is the distribution of XX? XX ~ N(,)What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)What is the probability that one randomly selected auto insurance is more than $929?a simple random sample of 40 auto insurance policies, find the probability that the average cost is more than $929.For part d), is the assumption of normal necessary? NoYes

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CNNBC recently reported that the mean annual cost of auto insurance is 979 dollars. Assume the standard deviation is 261 dollars, and the cost is normally distributed. You take a simple random sample of 40 auto insurance policies. Round your answers to 4 decimal places.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the probability that one randomly selected auto insurance is more than $929?
a simple random sample of 40 auto insurance policies, find the probability that the average cost is more than $929.
For part d), is the assumption of normal necessary? NoYes

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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