Question

A random sample of size 36 is to be selected from a population that has a mean μ = 50 and a standard deviation σ of 10.

   * a. This sample of 36 has a mean value of , which belongs to a sampling distribution. Find the shape of this sampling distribution.
   * b. Find the mean of this sampling distribution.
   * c. Find the standard error of this sampling distribution.
   * d. What is the probability that this sample mean will be between 45 and 55?
   * e. What is the probability that the sample mean will have a value greater than 48?
   * f. What is the probability that the sample mean will be within 3 units of the mean?

Answer 1

a. Sample mean not given, expect normality.

b. Without more info, expect sample mean = pop. mean

c. SEm = SD/√(n-1), but you can just use n

d, e, f. Z = (score-mean)/SEm

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