Question

Suppose that a survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax. Suppose that 40% of all adults in Ohio support the increase. We independently select 7 adults at random and record their status in supporting the increase. What is the probability that exactly 4 people support the increase in tax?

a. 0.2419
d. 0.4838
b. 0.5162
c. 0.1935

Answer 1

Option D) 0.1935

Explanation:

We are given the following information:

We treat adults in Ohio support the increase as a success.

P(Adults in Ohio support the increase) = 40% = 0.4

Then the number of adults follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 7

P(exactly 4 people support the increase in tax)

`P(x = 4)\\\\= \binom{7}{4}(0.40)^4(1-0.40)^3\\\\= 0.1935`

0.1935 is the probability that exactly 4 out of 7 adults in Ohio suppert the increase.

Thus, the correct answer is

Option D) 0.1935