CNNBC recently reported that the mean annual cost of auto insurance is $999. Assume the standard deviation is $200, and the cost is normally distributed. You take a simple random sample of 40 auto insurance policies. Round your answers to 4 decimal places.a. What is the distribution of $X$? $X \sim N(999, 200)$b. What is the distribution of $\bar{x}$? $\bar{x} \sim N\left(999, \frac{200}{\sqrt{40}} = 31.6228\right)$c. What is the probability that one randomly selected auto insurance is less than $1013? 0.5279d. In a simple random sample of 40 auto insurance policies, find the probability that the average cost is less than $1013. (Blank space for response)e. For part d), is the assumption of normal necessary? [ ] No [X] YesThe document contains calculations involving normal distribution and probabilities concerning auto insurance costs. The given distributions are standard normal distributions based on the mean and standard deviation provided. The problems are designed to test understanding of distribution properties and to calculate probabilities using the normal distribution.

From the information, given thatlet X denotes the cost which follows normal distribution with the…

Answered: d. a simple random sample of 40 auto…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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d. a simple random sample of 40 auto insurance policies, find the probability that the average cost is less than $1013. e. For part d), is the assumption of normal necessary? No Yes