Respuesta :
Given data
10 question true-false
Procedure
This is a binomial probability problem. Where we have two outcomes which are pass or fail. We want the probability to be less than or equal to 10%.
We assume that the probability of passing the exam is 60% which corresponds to 6/10 correct questions.
Recall that the probability for the binonamial distribution is
[tex]\text{NCn(p)}^np^{N-n}[/tex]where:
N = Total problems
n = problems you have correct
p = probability of getting problem right
Calculating for a score of 60%
[tex]\begin{gathered} P(X\ge x)=10C6(0.5)^6(0.5)^4 \\ P(X\ge x)=0.3769 \end{gathered}[/tex]Now, Let's try with a higher grade value to pass (80%)
[tex]\begin{gathered} P(X\ge x)=10C8(0.5)^8\cdot0.5^2 \\ P(X\ge x)=0.0546875 \end{gathered}[/tex]The passing grade would be 80%, i.e. getting 8 correct questions.
