A population hase a mean of 12 and a standard deviation of 2

A population hase a mean of 12 and a standard deviation of 24. A samle of size 36 is taken from this population Xbar is the sample mean.

FInd these porobabilities.

A) The mean is within 5 of the prpulation

B) Could we answer these questions for a sample size of 15? Explain.

A) The mean is within 5 of the prpulation

P(-5<xbar-mean<5) = P(-5/(24/sqrt(36)) <(xbar-mean)/(s/vn) <5/(24/sqrt(36)))

=P(-1.25<Z<1.25) =0.7887 (from standard normal table)

----------------------------------------------------------------------------------------------------------------------

B) Could we answer these questions for a sample size of 15? Explain.

No, because based on the central limit theorem we can use approximate to the normal distribution when the sample size is larger than 30