In: Statistics and Probability
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
years and a standard deviation of 0.4 years. He then randomly
selects records on 49 laptops sold in the past and finds that the
mean replacement time is 3.8 years.
Assuming that the laptop replacement times have a mean of 4 years
and a standard deviation of 0.4 years, find the probability that 49
randomly selected laptops will have a mean replacement time of 3.8
years or less.
P(M < 3.8 years) =
Enter your answer as a number accurate to 4 decimal places. NOTE:
Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted.
Based on the result above, does it appear that the computer store
has been given laptops of lower than average quality?
We have,
n = 49
Consider,
z-score = -3.5
Due to symmetry of z
From std normal(Z) table
Hence, P(X<3.8) = 0.0002
We observe that P(X<3.8) < 0.05, Therefore, the computer store has been given laptops of not lower than average quality.
Therefore,
Correct Answer: No. The probability of obtaining this data is high enough to have been a chance occurrence.