Question

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

Answer 1

Answer:

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

Step-by-step 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.