Answer:
0.1719
Step-by-step explanation:
Given that:
A quiz contains 20 questions and 10 questions have been answered rightly
We are to determine the probability of getting a total quiz score of 85%
i.e 0.85 (20) = 17
Let's not forget that 10 is correctly answered out of 17. that implies that we only have 7 more questions to make a decision on.
where;
n = 10,
p + q = 1, 0.5 + q = 1
q = 1 - 0.5
q = 0.5
Let X be the random variable that follows the binomial distribution. Then ;
[tex]P(X = x) =(^n_x) p^x q^{n -x}[/tex]
where x = 7
[tex]P(X \geq 7) =P(X=7)+P(X=8)+P(X=9)+P(X=10)[/tex]
[tex]P(X \geq 7) =(^{10}_7})\ 0.5^7 \ 0.5 ^{10-7} + (^{10}_{8})\ 0.5^8 \ 0.5 ^{10-8}+(^{10}_9})\ 0.5^9 \ 0.5 ^{10-9}+ (^{10}_{10}})\ 0.5^{10} \ 0.5 ^{10-10}[/tex]
P(X ≥ 7) = 0.1719
