Forty-four percent of U.S. adults believe the U.S. system

Chapter , Problem 3CQ

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QUESTION:

 Problem 3CQ

Forty-four percent of U.S. adults believe the U.S. system of justice is fair to most Americans. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who believe the U.S. system of justice is fair to most Americans is (a) exactly three, (b) at most four, and (c) more than seven.

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QUESTION:

 Problem 3CQ

Forty-four percent of U.S. adults believe the U.S. system of justice is fair to most Americans. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who believe the U.S. system of justice is fair to most Americans is (a) exactly three, (b) at most four, and (c) more than seven.

ANSWER:

Solution :

Step 1 of 3:

From the given information we know that we need to know the probability of a certain number with the characteristic in a finite sample.

Hence the corresponding distribution is the binomial distribution.

Here 44% of U.S. adults .

p = 44%

p =

p = 0.44 and

q = 1-p

q = 1-0.44

q = 0.56

Let n denotes 9 U.S. adults.

The binomial distribution formula is

P(X=k) =

P(X=k) =  

Our goal is:

We need to find the probability

a). P(X=3).

b). P(X4).

c). P(X>7).

a). Now we have to find P(X=3).

P(X=3) =

P(X=3) = 0.2206

Therefore, P(X=3) is 0.2206.


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