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 3.6 years and a standard deviation of 0.5 years. He then randomly selects records on 50 laptops sold in the past and finds that the mean replacement time is 3.4 years.

Assuming that the laptop replacement times have a mean of 3.6 years and a standard deviation of 0.5 years, find the probability that 50 randomly selected laptops will have a mean replacement time of 3.4 years or less.
P(M < 3.4 years) =
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.

Answer 1

Given that the laptop replacement times have a mean of = 3.6 years and a standard deviation of = 0.5 years, also the distribution is normal, now if a random sample of n =50 is selected to calculate the probability that mean replacement time of 3.4 years or less.

Thus P(M < 3.4 years) is calculated by finding the Z score at M = 3.4 which is calculated as:

Thus the probability is computed using the excel formula for normal distribution which is =NORM.S.DIST(-2.8284, TRUE), thus the probability is computed as 0.0023.

Based on the data the conclusion made is:

Yes. The probability of this data is unlikely to have occurred by chance alone.