Question

A manufacturer of alkaline batteries has observed that its batteries last for an average of 26 hours when used in a toy racing car. The amount of time is normally distributed with a standard deviation of 2.5 hours. What is the probability that the battery lasts longer than 28 hours?a. What is the probability that the battery lasts between 24 and 28 hours?b. What is the probability that the battery lasts longer than 28 hours?c. What is the probability that the battery lasts less than 24 hours?

Answer 1

a) 0.5763 b)0.2119 c)0.2119

Explanation:

In order to find find the probability that the battery lasts between 24 and 28 months, we have to find z

Z = (x – mean)/standard deviation

Le x be hours a battery last

P (24<x<28) = P((24– 26)/2.5 < z < (28– 26)/2.5)

P (24<x<28) = P(-0.8< z < 0.8)

Then we use the z table to find the area under the curve.

P (24<x<28) = 0.5763

the probability that the battery lasts longer than 28 hours

P (x>28) = P(z > (28– 26)/2.5)

P (x>28) = P(z > 0.8)

Then we use the z table to find the area under the curve.

P (x>28) = 0.2119

the probability that the battery lasts less than 24 hours

P (x<24) = P(z < (24– 26)/2.5)

P (x<24) = P(z < -0.8)

P (x<24) = 0.2119