Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n=75​, find the probability of a sample mean being greater than 213 if mu=212 and sigma=3.7.

Answer 1

Answer:

   ,   

=  

= 0.4272

Using central limit theorem,

P( < x) = P(Z < (x - ) / ( / sqrt(n) ) )

So,

P( > 213) = P(Z > ( 213 - 212) / ( 3.7 / sqrt(75) ) )

= P(Z > 2.34)

= 1 - P(Z < 2.34)

= 1 - 0.9904

= 0.0096

For a sample of n=75​, find the probability of a sample mean being greater than 213 if mu=212 and sigma=3.7 is 0.0096

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