Question

The mean lifetime of a tire is 41 months with the variance of 64. If 100 tires are sampled what is the probability that the mean of the sample would differ from the population mean by less than 0.88 months? Round your answer to four decimal places

Answer 1

Given data:

Mean: 41

Variance: 64

1. Find the standard deviation: the standard deviation is equal to the square root of the variance:

`\begin{gathered} \sigma=√(64) \\ \sigma=8 \end{gathered}`

2. Find the z-score corresponding to a difference from the mean of 0.88:

`z=(0.88)/((8)/(√(100)))=(0.88*√(100))/(8)=1.1`

3. As the probability could be a mean 0.88 over the mean or 0.88 below the mean, Use a z-score table to find the value corresponding to z=1.1 and z=-1.1:

Find the probability between those z-score values:

`0.8643-0.1357=0.7286`Then, the probability is 0.7286