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.

Probability distributions are used to represent the probability of events.

The distribution is given as:

(a) The event using probability notation

When a student sees 3 home alone movies, it means x = 3.

So, the probability notation is:

(b) Explain P(x > 3)

It means the event that a student has seen more than 3 home alone movies.

It is calculated as:

So, we have:

Hence, the value of P(x > 3) is 0.03

(c) Histogram

Start by calculating P(x = 3).

Using the complement rule, we have:

So, we have:

See attachment for the histogram

The shape is right-symmetric

(d) The expected value

This is calculated as:

So, we have:

This gives

It means that a student has seen the home alone movies an average time o 1.43 times

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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

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step-by-step explanation: