The Democrat and Chronicle reported that 25% of the flights arriving at the San

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. Calculate sigma(p) (sigma p-bar) with a sample size of 800 flights (to 4 decimals). What is the probability that the sample proportion lie between 0.22 and 0.28 if a sample of size 800 is selected (to 4 decimals)? What is the probability that the sample proportion will lie between 0.22 and 0.28 if a sample of size 400 is selected (to 4 decimals)?

Explanation / Answer

(a) p = 0.25, q = 0.75, n = 800

= (pq/n) = (0.25 * 0.75/800) = 0.0153

(b) z1 = (p1 - p)/ = (0.22 - 0.25)/0.0153 = -1.9596 and z2 = (0.28 - 0.25)/0.0153 = 1.9596

P(0.22 < p < 0.28) = P(-1.9596 < z < 1.9596) = 9500

(c) = (pq/n) = (0.25 * 0.75/400) = 0.0217

z1 = (p1 - p)/ = (0.22 - 0.25)/0.0217 = -1.3856 and z2 = (0.28 - 0.25)/0.0217 = 1.3856

P(0.22 < p < 0.28) = P(-1.3856 < z < 1.3856) = 0.8341

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