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

Read more about probability distribution at:

link

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

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130