Answer:
a) 0.1509
b) 0.8314
Step-by-step explanation:
Since there are only two options for each question, the probability that he guesses right is p = 0.50, and the probability that he guesses wrong is q = 0.50
There is a total of 15 questions in the test so we can use the formula for a binomial distribution with parameters n = 15, p = 0.5, q = 0.5
a) If he needs to score 10 or more correct to pass, what is the probability that he will fail the exam?
To find this probability we will need to find the probability:
P ( X < 10) or
(1 - P (x ≥10))
Remember that the formula for a binomial distribution is:
We can solve this by using the parameters given before and make x = 10, 11, 12, 13, 14, 15 and use the formula:
P(he fails the exam) = 1 - P (x≥10)
= 1 - (P(x=10) + P(x=11) + P(x=12) + P(x=13) + P(x=14) + P(x=15))
= 0.1509
b) Find the probability that he answers 6 to 11 inclusive)
We're going to use the same formula but we will do:
P (x = 6) + P (x = 7) + P (x = 8) + P (x = 9) + P (x = 10) + P (x = 11)
=0.1527 + .1964 + .1964 + 0.1527 + 0.0916 + 0.0416
= 0.8314
Therefore the probability that he answers 6 to 11 inclusive is 0.8314