Answered: CNNBC recently reported that the mean…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

CNNBC recently reported that the mean annual cost of auto insurance is 972 dollars. Assume the standard deviation is 102 dollars. You will use a simple random sample of 58 auto insurance policies.

Find the probability that a single randomly selected policy has a mean value between 977.4 and 997.4 dollars.
P(977.4 < X < 997.4) =

Find the probability that a random sample of size n=58 has a mean value between 977.4 and 997.4 dollars.
P(977.4 < ¯x < 997.4) =

Enter your answers as numbers accurate to 4 decimal places.

Expert Solution

Step 1

$Let us denote : X = the mean annual cost of auto insurance X follows a normal distribution with mean = 972 and standard deviation = 102 n = sample size = 58 \bar{X} follows a normal distribution with mean = 972 and standard deviation = \frac{102}{\sqrt{58}} = 13.3932561517$

Step 2

$A) The probability that a single randomly selected policy has a mean value between 977.4 and 997.4 dollars is : P (977.4 < X < 997.4) = P (\frac{977.4 - 972}{102} < Z < \frac{997.4 - 972}{102}) = P (0.0529411764706 < Z < 0.249019607843) = 0.0772$

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