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A quality control expert at LIFE batteries wants to test their new batteries. The design engineer...

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 87 minutes with a mean life of 538 minutes. If the claim is true, in a sample of 134 batteries, what is the probability that the mean battery life would be less than 547.9 minutes? Round your answer to four decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = 538

standard deviation = = 87

Sample size = n = 134

= 538

= / n = 87 134 =7.5156

P( < 547.9)

P ( - / ) < ( 547.9 - 538 / 7.5156 )

P ( z < 9.9 / 7.5156 )

P ( z < 1.32)

Using z table

= 0.9066

Probability = 0.9066

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