Question

3. .A multiple choice exam was given with 25 questions, each having only one correct answer out of 5 given alternatives. Assuming a student made random guesses for the answers, what is the probability that:

a. Exactly 20 questions were answered correctly?

b. 15 or fewer were answered right?

c. More than 10 were answered correctly?

d. Six or more are answered WRONG

4. Suppose your local state game commission has decided to limit the yearly ‘take’ of deer to 5 per hunter based on studies done over the last decade. If the probability of killing a deer on any given hunt is .06 (p), what is the probability that:

a. you could take your limit on the first hunt?

b. Zero deer are killed on the first hunt of the season?

c. Two or more deer are taken during the season?

d. fewer than five are bagged?

5.Your daughter has just decided to run for the senior class president. Out of 200 students, the probability that a student will vote for a female president has been estimated to be only 3 percent. Assuming that all students vote, what is the probability that she will receive

a. zero votes?

b. 10% or more of the votes?

c. less than 5% of the votes?

d. She receives exactly 10 vote

Answer 1

The the number of correct answers out of 25 questions has follows Binomial distribution with
The PMF of is

a) The probability that exactly 20 questions were answered correctly is

R command below:

> dbinom(20,25,0.2)
[1] 1.825533e-10

a) The probability that 15 or fewer questions were answered correctly is

R command below:
> pbinom(15,25,0.2)
[1] 0.9999979

c) The probability that more than 10 questions were answered correctly is

R command below:

> 1-pbinom(10,25,0.2)
[1] 0.00555492

d)Six or more are answered WRONG is equivalent to answering 19 or less questions correctly.

R command below:

> pbinom(19,25,0.2)
[1] 1