Question

The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25.

1. Calculate () with a sample size of 1,200 flights (to 4 decimals).


2. What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 1,200 is selected (to 4 decimals)?


3. What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 600 is selected (to 4 decimals)?

Answer 1

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Answer 2

1) (sqrt(.25*(1-.25))/1200) = .0125

2) .03/.0125 = 2.4 (z-score)
-.03/.0125 = -2.4 (z-score)
Find value using standard normal distribution table:
2.4 = .9918
-2.4 = .0082
.9918-.0082 = .9836

3) (sqrt(.25*(1-.25))/600) = .0177
.03/.0177 = 1.69 (z-score)
-.03/.0177 = -1.69 (z-score)
Find value using standard normal distribution table:
1.69 = .9545
-1.69 - .0455
.9545 - .0455 = .9090