Problem 1: (4 Pts)

Suppose you are organizing an alumni event for University of Dubai next week. You believe that attendance will depend on the weather on that day. You consider the following possibilities are appropriate:

Weather Probability = f(x) Attendance (X)
Terrible weather 0.2 500
Mediocre weather 0.6 1000
Great weather 0.2 2000

a. If X denotes the attendance, why is X a random variable?

b. What is the expected number of attendance?

c. Suppose that you will charge AED5 per attendee and the total cost of setting the event is AED 2,000. What is your expected profit?

d. What is the variance of attendance?

Problem 2: (3 Pts)

Your firm’s marketing manager believes that total sales X can be modeled using a normal distribution with mean u = AED 2.5 million and standard deviation σ = AED 300,000.

a. What is the probability that your firm’s sales will exceed AED 3 million?

b. Draw a sketch to illustrate your calculation.

Problem 3: (3 Pts)

The weight of a bag of corn chips is normally distributed with a mean of 21 ounces and a standard deviation of ½ ounces.

a) What is the probability that a bag of corn chips is less than 20 ounces?

b) What is the probability that a bag of corn chips weighs more than 22 ounces?

c) What is the probability that a bag of corn chips weighs between 20.75 and 22.25 ounces?