The mean life of a television set is 138 months with a variance of 324. If...

The mean life of a television set is 138 months with a variance of 324.

If a sample of 83 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 5.4 months? Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 138

standard deviation = = 18

= / n = 18 / 83 = 1.9758

= P[(-5.4) /1.9758 < ( - ) / < (5.4) / 1.9758)]

= P(-2.73 < Z < 2.73)

= P(Z < 2.73) - P(Z < -2.73)

= 0.9968 - 0.0032

= 0.9936

Probability = 0.9936

orchestra answered 1 year ago

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