The company claims that 52% (p = 0.52) of the Reese’s pieces are orange. One student took a sample of 30 and got 12 orange candies ( 40 . 0 ˆ  p ). Assume the company’s claim is true. 7. The company claims that the average weight of each piece is 8 . 0   grams with a standard deviation of 05 . 0   grams. Assume the company’s claim is true.

a. Calculate the mean and standard deviation of the sampling distribution of xfor SRSs of size 30.
b. Interpret the standard deviation in context.
c. What is the shape of the sampling distribution of x. Justify.
d. One student took a sample of 30 and got a mean weight of 0.78 grams. Assuming the company’s claim is true, what is the probability that a sample of 30 Reese’s pieces would have a mean weight of 0.78 or lower? Show work.
e. Does this student have convincing evidence that the company is lying about the mean weight of each piece? Explain.