Question

Sample surveys show that fewer people enjoy shopping than in the past. A survey asked a nationwide random sample of 2500 adults if they agreed or disagreed that “I like buying new clothes, but shopping is often frustrating and time-consuming.” Suppose that exactly 60% of all adult U.S. residents would say “Agree” if asked the same question. Let X = the number in the sample who agree. Estimate the probability that 1520 or more of the sample agree.

Answer 1

Given that, population proportion (p) = 0.60

sample size (n) = 2500

Mean and standard deviation of the sampling distribution of sample means are,

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We want to find, P(X ≥ 1520)

=> sample proportion = 1520/2500 = 0.608

Therefore, required probability is, 0.2071

Note: Using Excel we find,

P(Z < 0.8165) = NORMSDIST (0.8165) = 0.7929