## Question

Section I. Short-answers. Show work where appropriate for full credit.

Problem 1

The ounces of soda consumed by an adult next month are an example of a discrete random variable. True/False

Problem 2

Testing whether the computer is infected or not would be best described using binomial probability distribution. True/False

Problem 3

Which of the following can be represented by a discrete random variable?

A. The circumference of a randomly generated circle

B. The time of a flight between Chicago and New York

C. The number of defective light bulbs in a sample of five

D. The average distance achieved in a series of long jumps

Problem 14

The following table provides a probability distribution for the random variable x.

x P(X=x)

3 0.25

6 0.50

9 0.25

Compute E(X)

Problem 5

The following table provides a probability distribution for the random variable y.

y P(Y=y)

2 0.20

4 0.30

7 0.40

Compute E(Y), σ2, and σ.

Problem 6

Suppose an antibiotic has been shown to be 70% effective against a common bacteria.

a. If the antibiotic is given to 5 unrelated individuals with the bacteria, what is the probability that it will be effective in exactly 3? Interpret this probability.

b. What is the probability that the antibiotic will be effective in all five?

c. What is the probability that the antibiotic will be effective in none of the five?

d. What is the expected value (the mean number of patients out of five in whom the antibiotic is effective)? Use appropriate statistical notation(s).

e. What is the variance in the number of successes? Use appropriate statistical notation(s).

Problem 7

Suppose the average number of emails received by the junior analyst at your company is 5 emails/hour. Suppose the count of emails received can be modeled by a Poisson random variable.

a. What is the probability that this junior analyst receives exactly 5 emails in any given hour?

b. What is the standard deviation of this Poisson distribution?

Section II. Excel Work.

Using Excel to Compute Binomial Probabilities

• One option is to use Excel’s BINOM.DIST

Martin Clothing store

The store manager wants to determine the purchase decisions of next three customers who enter the clothing store. On the basis of past experience, the store manager estimates the probability that any one customer will make a purchase is .30.

1. Use Excel to compute P(X=0), P(X=1), P(X=2), and P(X=3)

Using Excel to Compute Poisson Probabilities

• One option is to use Excel’s POISSON.DIST

Arrivals at the drive-up teller window of a bank

The average number of cars arriving at the drive-up teller window of a bank in a 15 –minute period of time on weekday mornings is 10.

2. Use Excel to compute P(X=0), P(X=1), P(X=2), P(X=3) to P(X=10).

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