Question

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.2 years and a standard deviation of 0.6 years. He then randomly selects records on 38 laptops sold in the past and finds that the mean replacement time is 3.9 years. Assuming that the laptop replacement times have a mean of 4.2 years and a standard deviation of 0.6 years, find the probability that 38 randomly selected laptops will have a mean replacement time of 3.9 years or less.

Answer 1

Answer: 0.0010

Step-by-step explanation:

Given the following :

Population Mean(m) = 4.2 years

Sample mean (s) = 3.9

Standard deviation (sd) = 0.6

Number of samples (n) = 38

Calculate the test statistic (z) :

(sample mean - population mean) / (sd / √n)

Z = (3.9 - 4.2) / (0.6 / √38)

Z = (- 0.3) / (0.6 / 6.1644140)

Z = -0.3 / 0.0973328

Z = - 3.0822086

Z = - 3.08

From the z table :

P(Z ≤ - 3.08) = 0.0010