The Athletic Coping Skills Inventory (ACSI) is a test to measure psychological skills believed to influence athletic performance. Researchers E. Estanol et al. studied the relationship between ACSI scores and eating disorders in dancers in the article “Mental Skills as Protective Attributes Against Eating Disorder Risk in Dancers (Journal of Applied Sport Psychology, The study found that dancers. The study found that dancers’ 

ACSI scores are (approximately) normally distributed with mean 49.34 points and standard deviation 10.14 points.

a. Use the technology of your choice to simulate 1000 samples of four dancers’ ACSI scores each.

b. Find the sample mean of each of the 1000 samples obtained in part (a).

c. Obtain the mean, the standard deviation, and a histogram of the 1000 sample means.

d. Theoretically, what are the mean, standard deviation, and distribution of all possible sample means for samples of size 4?

e. Compare your answers from parts (c) and (d).