3. According to a survey, 68% of Americans say that they go to a movie theater at least once a month.
Suppose that this proportion is true for the current
American population.
a.
Let x be a binomial random variable that denotes
the number of Americans in a random sample of
12 who say that they go to a movie theater at
least once a month. What are the possible
values that x can assume?
b. Find the probability that exactly 9 Americans in
a random sample of 12 will say that they go to a
movie theater at least once a month.

The probability that exactly 9 Americans in  a random sample of 12 will say that they go to a  movie theater at least once a month

P( X = 9) =  0.007343

Step-by-step explanation:

Step(i):-

According to a survey, 68% of Americans say that  they go to a movie theater at least once a month.

Given proportion 'p' = 68% =0.68

                             q = 1-p = 1- 0.68 = 0.32

Given Number of Americans in a random sample

'n' = 12

Let 'X' be random variable of binomial distribution

Step(ii):-

Given r = 4

Given random sample 'n' =12

The probability that exactly 9 Americans in  a random sample of 12 will say that they go to a  movie theater at least once a month

using factorial notation

On calculation , we get

P( X = 9) =  0.007343

Final answer:-

The probability that exactly 9 Americans in  a random sample of 12 will say that they go to a  movie theater at least once a month

P( X = 9) =  0.007343

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

4+n=5

step-by-step explanation:

this is because the four is four hours and the n represents the 1 extra hour over the weekend.

b= i'm srry i don't know that one.

4+n=5 n=1 because if vernon plays 5 hours a week then 4+1=5 hours.

hope this : )