Question

Home Alone is a series of American Christmas family comedy films created by John Hughes. There are 5 Home Alone movies. Below is a probability distribution of the number of Home Alone movies watched by a very large sample of high school students. 0 1 2 3 4 5 Number of Home Alone Movies Watched Probability 0.15 0.42 0.32 ? 0.02 0.01
a. Write the event "the student has seen 3 Home Alone movies" using probability notation. Then find this probability.
b. Explain in words what P(X > 3) means. What is this probability?
c. Make a histogram of the probability distribution. Describe its shape.
d. Calculate and interpret the expected value of X.

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of Home alone movies (X)

Watched probability, p(x)

X : ___ 0 ____ 1 ____ 2 ____ 3 ___ 4 ___ 5

P(x) : _0.15 __ 0.42 __0.32 __? ___0.02 _0.01

a. Write the event "the student has seen 3 Home Alone movies" using probability notation. Then find this probability.

P(x = 3)

Since Σp(x) = 1

P(x =3) = 1 - (p(0)+p(1)+p(2)+p(4)+p(5))

P(x = 3) = 1 - (0.15 + 0.42 + 0.32 + 0.02 + 0.01)

P(x = 3) = 1 - 0.92

P(x = 3) = 0.08

b. Explain in words what P(X > 3) means. What is this probability?

P(x > 3) is the probability they a randomly chosen student has watched more than 3 home alone movies.

P(x > 3) = p(4) + p(5)

P( x > 3) = 0.02 + 0.01 = 0.04

d. Calculate and interpret the expected value of X.

E(X) = [Σ(X * p(x)]

(0*0.15) + (1*0.42) + (2*0.32) + (3*0.08) + (4*0.02) + (5*0.01) = 1.43

The avereage number of home alone movies watched is 1.43