Question 1 - Binomial Distribution

A university has found that 2.5% of its students withdraw without completing the introductory business analytics course. Assume that 100 students are registered for the course.

a) What is the probability that two or fewer students will withdraw?

b) What is the probability that exactly five students will withdraw?

c) What is the probability that more than three students will withdraw?

d) What is the expected number of withdrawals from this course?

Question 2 - Normal Distribution

Suppose that the return for a particular investment is normally distributed with a population mean of 10.1% and a population standard deviation of 5.4%.

a) What is the probability that the investment has a return of at least 20%?

b) What is the probability that the investment has a return of 10% or less?

A person must score in the upper 5% of the population on an IQ test to qualify for a particular occupation.

c) If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for this occupation?

Question 3 - Normal Distribution

According to a recent study, the average night's sleep is 8 hours. Assume that the standard deviation is 1.1 hours and that the probability distribution is normal.

a) What is the probability that a randomly selected person sleeps for more than 8 hours?

b) Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?

Question 4 - Normal Distribution

The time needed to answer a final examination in a particular college course is normally distributed with a mean of 160 minutes and a standard deviation of 25 minutes. Answer the following questions:

a) What is the probability of completing the exam in 120 minutes or less?

b) What is the probability that a student will complete the exam in more than 120

minutes but less than 150 minutes?

c) What is the probability that a student will complete the exam in more than 100

minutes but less than 170 minutes?

d) Assume that the class has 120 students and that the examination period is 180 minutes

in length. How many students do you expect will not complete the examination in the allotted time?