13.42 STDs. To track epidemics, the CDC requires physicians to report all cases of important transmissible diseases. In 2014, for instance, a total of 350,062 cases of the sexually transmitted disease (STD) gonorrhea were officially reported, 53% of which were individuals in their 20s. Assume that the value 53% remains the same every year. Researchers plan to take a random sample of 400 diagnosed cases of gonorrhea to study the risk factors associated with the disease. Call p^ the proportion of cases in the sample corresponding to individuals in their 20s.

1. What are the mean and standard deviation of the sampling distribution of p^ in random samples of size 400?

2. Explain why, under these conditions, the sampling distribution of p^ is approximately Normal.

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