54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

Where p is the probability of obtaining a "favorable outcome " x is the number of desired "favorable outcome " and n is the number of times the experiment is repeated. In this case n = 10 and p = 0.54.

(a) exactly five

This is:

[tex]x=5,\ n=10,\ p=0.54.[/tex]

So:

[tex]P(X=5)=\frac{10!}{5!(10-5)!}*0.54^x*(1-0.54)^{10-5}[/tex]

[tex]P(5)=0.238[/tex]

(b) at least six

This is: [tex]x\geq 6,\ n=10,\ p=0.54.[/tex]

[tex]P(x\geq 6)=P(6) + P(7)+P(8)+P(9) + P(10)[/tex]

[tex]P(x\geq 6)=0.478[/tex]

(c) less than four

This is: [tex]x< 4,\ n=10,\ p=0.54.[/tex]

[tex]P(x<4)=P(3) + P(2)+P(1)+P(0)[/tex]

[tex]P(x<4)=0.114[/tex]

shristiparmar1221 shristiparmar1221 · Answer 2 · 2021-12-09T09:50:39+01:00

This question is based on the probability. Therefore, the required probabilities are : (a) [tex]P(5) = 0.238[/tex], (b)[tex]P(x \geq 6) = 0.478[/tex] and (c) [tex]P(x <4) = 0.114[/tex].

Given:

54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults.

We have to find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

According to the question,

[tex]P(5) = 0.238\\P(x \geq 6) = 0.478\\P(x <4) = 0.114[/tex]

In this we have to calculate the probability using the binomial probability formula,

[tex]P(X=x) = \dfrac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]

Where, p is the probability of obtaining a "favorable outcome ", x is the number of desired "favorable outcome " and n is the number of times the experiment is repeated. In this case n = 10 and p = 0.54.

(a) exactly five

x=5, n= 10, p = 0.54

[tex]P(X=5)= \dfrac{10!}{5!(10-5)!} \times 0.5^{x} \times (1-0.54)^{10-5}[/tex]

P(X=5) = 0.238

(b) at least six

[tex]x\geq 6, n=10, p=0.54\\P(x\geq 6) = P(6) + P(7) + P(8) + P(9)+P(10)\\P(x\geq 6) = 0.478[/tex]

(c) less than four

[tex]x< 6, n=10, p=0.54\\P(x< 4) = P(3) + P(2) + P(1) + P(0)\\P(x< 4) = 0.114[/tex]

Therefore, the answers are : (a) [tex]P(5) = 0.238[/tex], (b)[tex]P(x \geq 6) = 0.478[/tex]

and (c) [tex]P(x <4) = 0.114[/tex].

For more details, please refer this link:

https://brainly.com/question/795909

54​% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

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54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.