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 p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the standard deviation of the sampling distribution of p hat ? Enter your answer as a decimal rounded to the hundredths place. The standard deviation of the sampling distribution of p hat is

The  shape of the sampling distribution of p hat is approximately Normal, because we would expect at least 10 success and 10 failures

The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.

approximately Normal, because we would expect at least 10 success and 10 failures. because they are dividing three times a week

A typical probability distribution in the natural world is the normal distribution, sometimes known as the bell curve. When the sample size is high enough, scientists often assume that a sequence of measurements obtained from a population would be regularly distributed.

The complete question is : 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 p hat = 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 p hat and why?

A. approximately Normal, because all sampling distributions are approximately Normal

B. approximately Normal, because we would expect at least 10 success and 10 failures

C. skewed to the right, because 0.31 is lower than 0.5

D. skewed to the left, because 0.31 is lower than 0.5

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