Question

..) An online website conducted a survey before the movie Toy Story 4 is d. The survey result showed that 40% of the people will go to a movie theater to L. Assume that 40% of all people will go to a movie theater to watch it. On a certain seven people at CSUSB Jack Brown Hall were asked if they will go to a movie theater w roy Story 4. Letx denote the number of people in this sample of seven who will go to a movie theater to watch Toy Story 4. (a) Would the graph of the probability distribution of x be skewed to the right, to the left, or be symmetric? Why? (Do not draw the graph.) (b) Using the binomial probabilities table, obtain the table of) probability distribution of (C) Using your table in (b), find the probability that at most 1 of the seven people will go to a movie theater to watch Toy Story 4 (write out the binomial formula before you use the table to find probabilities). (d) Use the particular formulas for binomial distribution to find the mean and standard deviation (rounded to 3 decimal places) of x. Don't forget about the units.

Answer 1

a)

X follow binomial distribution with n = 7 and p = 0.40

since p < 0.5

the graph will be right-skewed

b)

x	p
0	0.027994
1	0.130637
2	0.261274
3	0.290304
4	0.193536
5	0.077414
6	0.017203
7	0.001638

c)

P(X<= 1) = P(X = 0) + P(X = 1) = 0.027994 + 0.130637 = 0.15863

d)

mean = np = 7 * 0.4 = 2.8

sd = sqrt(npq) = sqrt(7 * 0.4*0.6) = 1.2961