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.
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.