Respuesta :
Answer:
0.3523 is the probability that the student will get less than 10 but more than 7 questions right.
Step-by-step explanation:
We are given the following information:
We treat answering the question correctly as a success.
P(guess of answer is correct) = 50% = 0.5
Then the number of questions 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 = 18
We have to evaluate:
[tex]P(7 < x < 10) \\= P(x = 8) + P(x = 9) \\= \binom{18}{8}(0.50)^8(1-0.50)^{10} + \binom{18}{9}(0.50)^9(1-0.50)^9\\= 0.1669 + 0.1854\\= 0.3523[/tex]
0.3523 is the probability that the student will get less than 10 but more than 7 questions right.
