The quality control manager at a computer manufacturing company believes that the mean life of a computer is 83 months, with a standard deviation of 9 months. if he is correct, what is the probability that the mean of a sample of 78 computers would be less than 82.06 months? round your answer to four decimal places.

0.1788

Step-by-step explanation:

As per given , we have

Let x be the random variable that represents the life of a computer.

Sample size : n= 78

Then, the z-score corresponds to x= 82.06 will be :-

[∵ ]

Required probability ( using standard z-value table ) :-

Hence, the probability that the mean of a sample of 78 computers would be less than 82.06 months = 0.1788