The mean life of a television set is 141

months with a variance of 256
.

If a sample of 71
televisions is randomly selected, what is the probability that the sample mean would be less than 136.3
months? Round your answer to four decimal places.

1 answer

To find the probability, we need to use the standard error of the mean formula:

Standard Error = sqrt(variance / sample size)

Standard Error = sqrt(256 / 71) = sqrt(3.6056) = 1.8971

Now we can calculate the z-score:

z = (sample mean - population mean) / standard error
z = (136.3 - 141) / 1.8971
z = -2.3989

Using a Z-table, we can find that the probability of getting a z-score less than -2.3989 is approximately 0.0081.

Therefore, the probability that the sample mean would be less than 136.3 months is 0.0081.