Answer:
a) 0.251
b) 0.483
c) 0.0994
Step-by-step explanation:
We are given the following information:
We treat adult adults trusting national newspapers to present the news fairly and accurately as a success.
P(Adult trust) = 60% = 0.6
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
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 = 9
a) exactly five
[tex]P(x = 15) = \binom{9}{5}(0.6)^{5}(1-0.6)^{9-5} = 0.2508 \approx 0.251[/tex]
b) at least six
We have to evaluate
[tex]P(x \geq 6) = P(x = 6) + P(x = 7) + P(x=8) + P(x=9) \\= \binom{9}{6}(0.6)^6(1-0.6)^3 + \binom{9}{7}(0.6)^7(1-0.6)^2 + \binom{9}{8}(0.6)^8(1-0.6)^1 +\binom{9}{9}(0.6)^9(1-0.6)^0\\= 0.482609 \approx 0.483[/tex]
c) less than four
We have to evaluate
[tex]P(x < 4) = P(x = 0) + P(x = 1) + P(x=2) + P(x=3) \\= \binom{9}{0}(0.6)^0(1-0.6)^9 + \binom{9}{1}(0.6)^1(1-0.6)^8 + \binom{9}{2}(0.6)^2(1-0.6)^7 +\binom{9}{3}(0.6)^3(1-0.6)^6\\= 0.099352 \approx 0.0994[/tex]
Probabilities are used to determine the chances of events
The proportion (p) is given as:
p = 60%
The sample size (n) is given as:
n = 9
The probability is then calculated as:
[tex]P(x) = ^nC_x * p^x * (1 -p)^{n-x}[/tex]
So, we have:
a. exactly five.
[tex]P(x = 5) = ^9C_5 * (60\%)^5 * (1 -60\%)^{9-5\\[/tex]
[tex]P(x = 5) = 0.251[/tex]
b. at least six
[tex]P(x \ge 6) = P(6) + P(7) + P(8) + P(9)[/tex]
[tex]P(x \ge 6) = 0.483[/tex]
c. less than four.
[tex]P(x < 4) = P(0) + P(1) +P(2) + P(3)[/tex]
[tex]P(x < 4) = 0.099[/tex]
Read more about probabilities at:
https://brainly.com/question/25870256
