A random sample of 81 observations is drawn from a population with a mean of 104...

A random sample of 81 observations is drawn from a population with a mean of 104 and a variance of 156.25.

a) State the distribution of the sample mean, ?̅. (Show any conditions that you have checked.)

b) Calculate the probability that the sample mean is at most 102.5.

c) Calculate the probability that the sample mean is between 103.5 and 105.8.

Solutions

Expert Solution

Given that, mean = 104 and

variance = 156.25

=> standard deviation

sample size (n) = 81

a) The distribution of the sample mean is approximately normal because, sample size is greater than 30 and also population standard deviation is known.

Mean and standard deviation of the sampling distribution of sample mean are,

b) We want to find,

Therefore, required probability is 0.1401

c) We want to find,

Therefore, required probability is 0.5438

milcah answered 9 months ago

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