Question

The mean lifetime of a tire is 48 months with a standard deviation of 77 months. If 147 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.83 months?

Answer 1

0.55199

Explanation:

When we have a random number of samples, We solve using z score formula

z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation

n is random number of samples

z = 0.83/77/√147

z = 0.13069

Probabilty value from Z-Table:

P(x<48.83) = 0.55199

The probability that the mean of the sample would differ from the population mean by less than 0.83 months is 0.55199