Question

Suppose an actual census showed that 18.4% of the households in California have incomes in excess of $50,000.

The probability that the sample proportion will be 0.22 or greater for a random sample of 750 households is:

a) 0.0055. b) 0.9945. c) 0.9949. d) 0.0041. e) None

Answer 1

This is a Normal Distribution problem.

P = 0.184 (18.4% as a decimal)

n = 750

Standard Deviation = Sqrt (P*(1-p) /n) = Sqrt(0.184*0.816/750) = 0.014149

Normal Distribution = (0.22-0.184)/0.0141 49 = 0.036/0.0141 = 2.544

2.544 on the Standard Normal Table = 0.9945

Probability sample is greater: 1 - 0.9945 = 0.0055

Answer is a) 0.0055