Question

1,

There is a 170 choice test required to enter the med school.

Jack refers to a school that needs a score of 70% or more for admission to the test.

Suppose there are four choices for each problem, and they guess at random for each question.

a. Which kind of distribution can be modeled after that?

B. How many questions will Jack have to answer in order to pass the test? What is the probability that they receive a high enough exam score to be admitted to nursing school?

Answer 1

a) As the person is guessing equally likely from all the 4 choices, therefore the probability to get any question correct is given as: 1/4 = 0.25. Therefore the number of correct questions out of 170 questions here is modelled as:

$X \sim Bin(n = 170, p = 0.25)$

Therefore this is a binomial probability with parameters n = 170 and p = 0.25

b) The number of questions that will have to be answered correctly is computed here as:
= 70% of 170 = 0.7*170 = 119

Therefore 119 questions are needed to be answered correctly here.

The probability that a high enough score is admitted to nursing school is computed here as:
P(X >= 119) = 1 - P(X <= 118)

This is computed in EXCEL here as:
=1-binom.dist(118,170,0.25,TRUE)

0 is the approximate probability here.

Therefore 0 is the required probability here.