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someone claims to have developed a new lightbulb whose mean lifetime is 1800 hours with a...

someone claims to have developed a new lightbulb whose mean lifetime is 1800 hours with a standard deviation of 100 hours. a sample of 100 of these bubs is tested. The sample mean lifetime is 1770 hours. if the claim is true , what is the probability of obtaining a sample mean that is less than 1770 hours ? Provide your answer in percent.

Math   Statistics-And-Probability   
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Answer #1

Given data are

Population mean = 1800 hours

Population sd =100 hours

sample n =100

Sample mean =1770 hours

In a z normal distribution z =

Z=(1770-1800)/(100/)

= - 30/10 = -3

Then

p (z < -3) =0.00135 = 0.135%

Then the probability of obtaining a sample mean that is less than 1770 is 0.135%

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