Probability

Another one I got wrong: I got the answers I just need someone to walk me through it...much appreciated!

A population with a mean 1,250 and standard deviation of 400 is known to be highly skewed to the right. If a random sample of 64 items is selected from the population, what is the probability that the sample mean will be less than 1,325.

The answer is:
From a standard normal table, the probability associated with z-1.50=0.4332
therefore, P(x<1325)=P(z<1.5)=0.5+0.4332=0.9332

Hi Lisa,

as you are dealing with a sample,
you use Z = (x-mean)/(SD/sqrt[n])
n=64, so sqrt(64) is 8 and 400/8 = 50.

x-mean is 1325-1250 = 75 and 75/50 = 1.5.

Hence p(Z<1.5) = 0.9332 from the z tables.

Though the population is skewed, the distribution of sample means will be normally distributed.
I ought to have first asked you to show your work, however.