Answer:
a. 0.011 or 1.1%
b. 31.56% or 0.3156
c. 99.94% or 0.9994
d. 3.42% or 0.0342
Step-by-step explanation:
Given
Number of multiple choice questions = 100
Probability of success for students who have attended lectures and done their homework = 0.85
a. Using binomial distribution
Probability of correctly answering 90 or more questions out of 100
Since,
In Binomial Distribution
where
and
Probability is therefore 1.1% or 0.011
b. Probability of correctly answering 77 to 83 questions out of 100
The probability is therefore 31.56% or 0.3156
c. Probability of correctly answering more than 73 questions out of 100
The probability is therefore 99.94% or 0.9994
d. Assuming that the student has answered randomly
Probability of success = 1/5 = 0.2
Probability of failure = 1 - 0.2 = 0.8
Probability of answering 28 or more questions correctly
The probability is therefore 3.42%