Question

Consider taking a simple random sample of 100 college students, asking them number of movies they watched last week (x) and then calculating the sample mean.

Can we expect X to have normal distribution? Why or why not?

Can we expect the distribution of X¯ to be normal? Why or why not?

Answer 1

Yes, we expect X to have normal distribution.

Explanation: Because if we ask to student number of movies they watched last week few of them will say not watched, one movie watched. but most of student says two movies watched, three movie watched and four movies watched. again few of them says five movies watched, six movies watched and seven movies watched. Thus we see the histogram of number of movies watched last week it will be symmetrical and Normal.

Yes. we expect the distribution of X¯ to be normal.

Explanation: Because the distribution of sample mean (X¯ ) is approximately normal.