Answer to Question #194548 in Macroeconomics for fahmida

Question

2. Suppose that in Bangladesh, fifty percent people believe that the cricket team of Bangladesh  can defeat any cricket team around the world. For a sample of 20 people, make the following  calculations. a. Compute the probability that exactly 12 people believed that the cricket team of Bangladesh  can defeat any cricket team around the world. b. Compute the probability that no more than five people believed that the cricket team of  Bangladesh can defeat any cricket team around the world. c. How many people would you expect to say that the cricket team of Bangladesh can defeat any  cricket team around the world? d. Compute the variance and standard deviation of the number of people who believed that the  cricket team of Bangladesh can defeat any cricket team around the world.

Answer 1

Let, X=the number of people who believe that the cricket team of

 Bangladesh can defeat any cricket team around the world.

n=number of trials=20

p=probability of success=50%=0.50

Each people is independent of the other people. 

So, X follows a binomial distribution with n=20 and p=0.50

a) The probability that exactly 12 people believed that the cricket team

 of Bangladesh

can defeat any cricket team around the world is

$P(X=12)$

$=(20C12)(0.50)^{12}(1−0.50)^{20−12}$

$=0.12013435364$

$Answer(a): 0.12013435364$

b) The probability that no more than 5 people believed that the

 cricket team of Bangladesh 

can defeat any cricket team around the world is

$P(X≤5)$

$=\textstyle\sum_{r=0}^5(20C5)(0.50)^{r}(1−0.50)^{20−r}$

$Answer(b): 0.0206947326$

c) The number of people I would expect to say that the cricket team

 of Bangladesh

can defeat any cricket team around the world is$= E(X)=np=20×0 .50=10$

$Answer(c): 10$

d) Variance$= Var(X)=np(1−p)=20×0.50×(1−0.50)=5$

Standard deviation$=\sqrt{variance}=\sqrt{5}$

Variance=5

Standard deviation$=\sqrt{5}$