Question

Let X represent the number of times a student visits a bookstore in a one-month period. Assume that the probability distribution of X is as follows: Let X represent the number of times a student visits a bookstore in a one-month period. Assume that the probability distribution of X is as follows:

x	0	1	2	3
p(x)	0.15	0.20	0.45	?

Find the mean µ  and the standard deviation  σ  of this distribution.

1. What is the probability that the student visits the bookstore at least twice in a month?

(1 mark)

           

2. What is the probability that the student visits the bookstore at most ones in a month?

(1 mark)

Answer 1

X; Number times a student visits a book store in a month

Probability distribution of X :

x	0	1	2	3
p(x)	0.15	0.20	0.45	?

For p(x) to be valid probability mass fucntion;

Then

0.15+0.20+0.45+? = 1 ;

? = 1-(0.15+0.20+0.45) = 1 - 0.80 =0.20

x	0	1	2	3
p(x)	0.15	0.20	0.45	0.20

Mean : :

Variance of X = E(X2) - E(X)2

Variance of X = E(X2) - E(X)2 = 3.8 - 1.72 = 3.8 - 2.89=0.91

Standard deviation of the distribution :

a. Probability that the students visits the books tores at least twice a month = P(X2) = 1-[P(X=0]+P(X=1]]

P(X=0) = p(0) =0.15

P(X=1) = p(1) = 0.20

P(X2) = 1-[P(X=0]+P(X=1]] =1 - [0.15+0.20]=1-0.35=0.65

Probability that the students visits the books tores at least twice a month = 0.65

a. Probability that the student visits the bookstore at most ones in a month = P(X1)

P(X1) = P(X=0)+P(X=1) = p(0)+p(1) =0.15+0.20 =0.35

Probability that the student visits the bookstore at most ones in a month = 0.35