Question

You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 32 years of rainfall for California and a sample of 48 years of rainfall for New York has been taken.

b.What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)

c.What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

d.In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?

Answer 1

b) P(21 < < 23)

= P((21 - )/() < ( - )/() < (23 - )/())

= P((21 - 22)/(4/) < Z < (23 - 22)/(4/))

= P(-1.41 < Z < 1.41)

= P(Z < 1.41) - P(Z < -1.41)

= 0.9207 - 0.0793

= 0.8414

c) P(41 < < 43)

= P((41 - )/() < ( - )/() < (43 - )/())

= P((41 - 42)/(4/) < Z < (43 - 42)/(4/))

= P(-1.73 < Z < 1.73)

= P(Z < 1.73) - P(Z < -1.73)

= 0.9582 - 0.0418

= 0.9164

d) The probability in part(c) is greater. Because the sample size is greater for part(c).