Question

A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise

at least 3 times a week. A simple random sample of 250 students was selected. Let a = the proportion of students in
the sample who claimed to work out at least 3 times a week.
What is the shape of the sampling distribution of and why?
O approximately Normal, because all sampling distributions are approximately Normal
o approximately Normal, because we would expect at least 10 success and 10 failures
O skewed to the right, because 0.31 is lower than 0.5
O skewed to the left, because 0.31 is lower than 0.5

Answer 1

The shape of the sampling distribution of a proportion is approximately normal.

Step-by-step explanation:

The shape of the sampling distribution of a proportion depends on the conditions of the sampling distribution. In this case, the conditions state that the sample size is large (n = 250) and the success-failure condition is satisfied (expected number of successes and failures is greater than or equal to 10). When these conditions are met, the sampling distribution of the proportion is approximately normal.

Answer 2

B

Step-by-step explanation: