The makers of Skittles claim that 20% of Skittles candies are orange. Suppose this claim is true. You select a random sample of 30 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample.

a. Identify the mean of the sampling distribution of p̂.

b. Calculate and interpret the standard deviation of the sampling distribution of p̂. Verify that the 10% condition is met.

c. Describe the shape of the sampling distribution of p̂. Justify your answer.