Question

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that:

(a) the first question she gets right is the 5th question?


(b) she gets all of the questions right?


(c) she gets at least one question right?


What is the area under the standard normal distribution for each region?


(a) Z< -1.65


(b) Z>1.5


(c) -1.1

(d) |Z|>1.3

Answer 1

a) 0.079

b) 0.001

c) 0.763

Explanation:

The probability of answering wrong is 3/4=0.75.

The probability of answering right is 1/4=0.25.

a) The probability that the first question she gets right is the fifth question.

This mean that the first four questions are answered wrong.

Then

`P=0.75^4*0.25=0.3164*0.25=0.0791`

b) The probability that she gets all of the question right

`P=0.25^5=0.001`

c) The probability that she gets at least one question right. We can calculate that by substracting from 1 the probability that she gets all wrong.

`P=1-0.75^5=1-0.2373=0.7627`

Area under the standard normal distribution for each region:

a) P(Z<-1.65)=0.04947

b) P(Z>1.5)=0.06681

c) P(Z<-1.1)=0.13567

d) P(|Z|>1.3)=0.1936