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A population has a mean of 180 and a standard deviation of 24. A sample of...

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be between 183 and 186 is

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Expert Solution

Solution :

Given that,

mean = = 180

standard deviation = = 24

n = 64

= = 180

= / n = 24 / 64 = 3

P(183 < < 186 )  

= P[(183 - 180) /3 < ( - ) / < (186 - 180 ) /3 )]

= P( 1< Z < 2 )

= P(Z < 2 ) - P(Z < 1 )

= 0.9772 - 0.8413 = 0.1359

Probability = 0.1359  

orchestra answered 2 years ago
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