Question

In: Statistics and Probability

The lifetimes of a certain electronic component are known to be normally distributed with a mean...

The lifetimes of a certain electronic component are known to be normally distributed with a mean of 1,400 hours and a standard deviation of 600 hours. For a random sample of 25 components the probability is 0.6915 that the sample mean lifetime is less than how many hours?

A)1345

B)1460

C)1804

D)1790

Solutions

Expert Solution

Given that,

mean = = 1400

standard deviation = = 600

n = 25

= 14000

= / n = 600 /25=120

Using standard normal table,

P(Z < z) = 0.6915

= P(Z < z) = 0.6915  

= P(Z < 0.5) = 0.6915

z = 0.5 Using standard normal table,

Using z-score formula  

= z * +   

= 0.5 *120+1400

= 1460

orchestra answered 2 years ago
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