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 3.9 years and a standard deviation of 0.4 years. He then randomly selects records on 53 laptops sold in the past and finds that the mean replacement time is 3.7 years.

Assuming that the laptop replacement times have a mean of 3.9 years and a standard deviation of 0.4 years, find the probability that 53 randomly selected laptops will have a mean replacement time of 3.7 years or less.
P(M < 3.7 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

Solution :

Given that,

mean = =3.9

standard deviation = = 0.4

n = 53

_M = 3.9

_M = / n = 0.4 /53 = 0.0549

P(M < 3.7 )

P (M - M) / M < (3.7 - 3.9) / 0.0549))

= P( Z < -0.2 /0.0549)

= P(Z < -3.64)   

=0.0001

Probability =0.0001

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