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
Probability distributions are used to represent the probability of events.
The distribution is given as:
[tex]\mathbf{Homes \to Probability}[/tex]
[tex]\mathbf{0 \to 0.15}[/tex]
[tex]\mathbf{1 \to 0.42}[/tex]
[tex]\mathbf{2 \to 0.32}[/tex]
[tex]\mathbf{3 \to ?}[/tex]
[tex]\mathbf{4 \to 0.02}[/tex]
[tex]\mathbf{5 \to 0.01}[/tex]
(a) The event using probability notation
When a student sees 3 home alone movies, it means x = 3.
So, the probability notation is: [tex]\mathbf{P(x = 3)}[/tex]
(b) Explain P(x > 3)
It means the event that a student has seen more than 3 home alone movies.
It is calculated as:
[tex]\mathbf{P(x > 3) = P(4) + P(5) }[/tex]
So, we have:
[tex]\mathbf{P(x > 3) = 0.02 + 0.01}[/tex]
[tex]\mathbf{P(x > 3) = 0.03}[/tex]
Hence, the value of P(x > 3) is 0.03
(c) Histogram
Start by calculating P(x = 3).
Using the complement rule, we have:
[tex]\mathbf{P(x = 3) = 1 - P(0)- P(1) - P(2) - P(x > 3)}[/tex]
So, we have:
[tex]\mathbf{P(x = 3) = 1 - 0.15 - 0.42 - 0.32 - 0.03}[/tex]
[tex]\mathbf{P(x = 3) = 0.08}[/tex]
See attachment for the histogram
The shape is right-symmetric
(d) The expected value
This is calculated as:
[tex]\mathbf{E(x) = \sum x P(x)}[/tex]
So, we have:
[tex]\mathbf{E(x) = 0 \times 0.15 + 1 \times 0.42 + 2 \times 0.32 + 3 \times 0.08 + 4 \times 0.02 + 5 \times 0.01}[/tex]
This gives
[tex]\mathbf{E(x) = 1.43}[/tex]
It means that a student has seen the home alone movies an average time o 1.43 times
Read more about probability distribution at:
https://brainly.com/question/795909
