Every year at the AP Statistics Exam reading apparel is sold to commemorate the event. Based on historical data, we know that 56% of teachers will make an apparel purchase. This year, the organizers have decided to select a random sample of 50 teachers. If a selected teacher made an apparel purchase, they will be given a prize. What is the probability that more than 60% of the selected teachers will win a prize? (A) Approximately 0 (B) 0.007 (C) 0.284 (D) 0.468 (E) 0.600

C

Step-by-step explanation:

The correct answer is c. To carry out this calculation, we begin by describing the sampling distribution of the sample proportion. The sample size is n=50 and the population proportion of teachers who made an apparel purchase is .56. Shape: because np=(50)(.56)=28 and n(1-p)=(50)(.44) are both at least 10, the shape of the sampling distribution of the population proportion is approximately normal. Center: p=.56. Variability: the standard deviation of the sample proportion is approximately .0702. normalcdf(loser: .6, upper: 1000, mean: .56, SD: .0702)=.284.

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