Question

A May 2000 Gallup poll found that 38% of the people in a random sample of 1,012 adult Americans said that they

believe in ghosts. Suppose that three adults will be randomly selected with replacement from the group that responded
to this poll, and the number of adults (out of the three) who believe in ghosts will be observed.
10. Develop a discrete probability distribution for the number of adults in the sample who believe in ghosts
11. Calculate the probability that at least one adult, but at most two adults, in the sample believes in ghosts. Interpret
this probability in context.
12. Out of the three randomly selected adults, how many would you expect to believe in ghosts? Interpret this
expected value in context.

Answer 1

10.

x P(X)

0 0.238

1 0.438

2 0.269

3 0.055

11.

0.707

There is 70.7% chance that at least one but at most two adults in the sample believes in the ghost

12.

1.14≅1

There will be one adult out of three we expect to believe in the ghost

Explanation:

The probability distribution is constructed using binomial distribution.

We have to construct the probability distribution of the number adults believe in ghosts out of three adults. so,

x=0,1,2,3

n=3

p=probability of adults believe in ghosts=0.38

The binomial distribution formula

nCxp^xq^n-x=3cx0.38^x0.62^3-x

is computed for x=0,1,2,3 and the results depicts the probability distribution of the number adults believe in ghosts out of three adults.

x P(X)

0 0.238

1 0.438

2 0.269

3 0.055

11.

P(at least one but at most two adults in the sample believes in the ghost )= P(x=1)+P(x=2)=0.437+0.269=0.707

P(at least one but at most two adults in the sample believes in the ghost )=70.7%

12. E(x)=n*p

here n=3 adults and p=0.38

E(x)=3*0.38=1.14

so we expect one adult out of three will believe in the ghosts.