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?

Question

Mathematics

Gianni Fox

6 August, 00:06

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?

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Answers (1)

Know the Answer?

Kiera · Answer 1

a) 0.5763 b) 0.2119 c) 0.2119

Step-by-step 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
P (24
Then we use the z table to find the area under the curve.

P (24
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