An agricultural economist is interested in determining the average diameter of peaches produced by a particular tree. A random sample of 50 peaches is taken and the sample mean calculated. Suppose that the average diameter of peaches on this tree is known from previous years' production to be 75 millimeters with a standard deviation of 15 millimeters. What is the probability that the sample mean exceeds 78 millimeters?

Question

An agricultural economist is interested in determining the average diameter of peaches produced by a particular tree.  A random sample of 50 peaches is taken and the sample mean calculated.  Suppose that the average diameter of peaches on this tree is known from previous years' production to be 75 millimeters with a standard deviation of 15 millimeters.  What is the probability that the sample mean exceeds 78 millimeters?

PsyDAG · Answer

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.