Statistical Abstracts (117th edition) reports sale price of unleaded gasoline (in cents per gallon) at the refinery. The distribution is mound-shaped with mean μ = 80.04 cents per gallon and standard deviation, σ = 4.74 cents per gallon.

Question

(a) Are we likely to get good results if we use the normal distribution to approximate the distribution of sample means for samples of size 9? Explain.

(b) Find the probability that for a random sample of size 9, the sample mean price will be between 79 and 82 cents per gallon.

(c) Find the probability that for a random sample of size 36, the sample mean price will be between 79 and 82 cents per gallon.

(d) Compare your answers for parts (b) and (c) and give a reason for the difference.

Answer 1

a. A larger sample would give a better estimate.

b. Z = (score-mean)/SEm

SEm = SD/√n

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

c. Use similar process.

d. See a.