In a particular large midwest city, a simple random sample of 400 people reveals that 128 of them know how to ski. 1. a 99.8% confidence interval for the proportion of people in the city who know how to ski is

a. (0.272, 0.368)
b. (0.304, 0.336)
c. (0.248, 0.392)
d. (0.282, 0.358)

Answer

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Step-by-step explanation:

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c. (0.248, 0.392)

Step-by-step explanation:

We have a large simple random sample of n = 400 people and 128 of them know how to ski. Let p be the true proportion of people in the city who know how to ski, then is an estimated of p. An approximation of the standard deviation of is . Because we want a 99.8% confidence interval for the proportion of people in the city who know how to ski, we have that , we need , i.e., the 0.1th quantile of the standard normal distribution. Therefore, the 99.8% confidence interval is given by , i.e., (0.2480, 0.3920)