Questions:
1. Given the following probability distribution:
X
0
1
2
3
4
P(x)
0.25
0.41
?
0.03
0.01


a) What is a probability distribution?
A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment
b) Describe this probability distribution X
P(X = 0) = 0.25 )
( P(X = 1) = 0.41 )
( P(X = 2) = 0.30 )
( P(X = 3) = 0.03 )
( P(X = 4) = 0.01 )


c) Find the probability that X equals 2
1-0.7=
P(X = 2) = 0.30 )
d) Find the probability that X is at least 1
=0.41+0.3+0.03+0.01
= (P(X \geq 1) = 0.75 )


e) Find the probability that X is at most 1
P(X < 1 ) = P ( x = 0) + P ( x = 1) = .25 + .41 = .66
f) Find the probability that X is more than 2
P ( X > 2 ) = P ( x = 3 ) + P ( x = 4 ) = .04
g) Determine all possible unusual events using the probability
P ( x = 3 ) = .03 and P ( x = 4) = .01. They both are under .05 causing them become unusual
h) Find the mean, variance, and standard deviation of X
i) Determine all possible unusual events using the mean and standard deviation

2. The graph of the discrete probability below represents the number of live births by mothers 41 to 45 years old in 2019.
Number of Live Births, X
Probability, P(x)
1
0.237
2
0.254
3
0.167
4
0.111
5
0.104
6
0.034
7
0.041
8
0.052



If a mother is randomly selected:
a) What is the probability that she has had her fourth live birth?
Probability : 11.1%
b) What is the probability that she has had at most four live births?
Probability: 0.769 = 76.9%
c) Compute the mean and standard deviation of the distribution using StatCrunch
Mean : 3.117 Standard Deviation: 1.994
If 2 mothers is randomly selected:
d) What is the probability that one of them has had her fourth live birth?
0.111
e) What is the probability that both of them have had at most four live births?
(0.769^2 = 0.591) (rounded to 59.1%).