MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

Answer:[tex]P(5)=0.238[/tex][tex]P(x\geq 6)=0.478[/tex][tex]P(x<4)=0.114[/tex]Step-by-step explanation:In this case we can calculate the probability using the binomial probability formula[tex]P(X=x)=\frac{n!}{x!(n-x)!}*p^x*(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 fiveThis 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 sixThis 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 fourThis 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]