Question

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 6724 with a mean life of 645 minutes. If the claim is true, in a sample of 152 batteries, what is the probability that the mean battery life would differ from the population mean by more than 8 minutes? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = $\mu$ = 645

standard deviation = $\sigma$ = 82

P(637 < x < 653) = P((637 - 645)/ 82) < (x - $\mu$ ) /$\sigma$  < (653 - 645 ) / 82) )

= 1 - (P(-0.098 < z < 0.098) )

= 1 - (P(z < 0.098) - P(z < -0.098))

= 1 - (0.5390 - 0.4610)

= 1 - 0.0780

= 0.9220

Probability = 0.9220