Question

The mean output of a certain type of amplifier is 165 watts with a variance of 144.

If 78 amplifiers are sampled, what is the probability that the mean of the sample would be greater than 163.7 watts? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 165

variance = 144

standard deviation = = 12

n = 78

= 165 and

= / n = 12 / 78

P( > 163.7) = 1 - P( < 163.7)

= 1 - P(( - ) / < (163.7 - 165) / 12 / 78 )

= 1 - P(z < -0.9568)

= 1 - 0.1693

= 0.8307

Probability = 0.8307