The standard deviation of the lifetime of a particular brand of car battery is 4.3 months. A random sample of 10 of these batteries is taken. Assuming that the lifetimes of all batteries of this brand are normally distributed, what is the probability that the mean lifetime for this sample is within 1 mouth of the mean lifetime for all batteries of this brand?

a. 0.019

b. 0.184

c. 0.519

d. 0.538

e. 0.769

Question

Carl Dean

Mathematics

28 October, 21:21

The standard deviation of the lifetime of a particular brand of car battery is 4.3 months. A random sample of 10 of these batteries is taken. Assuming that the lifetimes of all batteries of this brand are normally distributed, what is the probability that the mean lifetime for this sample is within 1 mouth of the mean lifetime for all batteries of this brand?

a. 0.019

b. 0.184

c. 0.519

d. 0.538

e. 0.769

+2

Answers (1)

Know the Answer?

Julian Harvey · Answer 1

d. 0.538

Step-by-step explanation:

Given information.

Standard deviation is 4.3

Random sample of 10

Consider the following calculations

P (sample mean is within 1 month of population mean) =

P (-1*sqrt (10) / 4.3
=0.538