Answer:
a) 0.352% probability of the student passing
b) 5
c) 1.875
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student answers it correctly, or he answers it wrong. The probability of correctly answering a question is independent from the probability of correctly answering other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is:
The variance of the binomial distribution is:
For each question, there are four choices.
One choice is correct, so
a. Find the probability of the student passing for n = 10.
0.7*10 = 7
This is when
0.352% probability of the student passing
b. Find the expected number of questions answered correctly for n = 20.
Here we have n = 20. So
c. Find the variance for the number of questions answered correctly for n = 10.
Here we have n = 10.