**Net Income (X) ** **Probability (f(X))**

**-1.5 0.20**

**0 0.25 **

** 1 0.40 **

** 2 W **

a. Find the value of W.

b. What is the probability that the company has a net income of less than $1 million in the coming year?

c. What is the probability that the company is not profitable (net income less than 0) in the coming year?

d. What is the probability that the company makes more than $0.5 million in the coming year?

e. What is the expected net income for ABC Limited, i. e, what is the expected value of this probability distribution?

f. What is the standard deviation of this probability function?

**2. An amusement park in Ontario conducted market research on the frequency of visits to the park by families who live within a 50 kilometers radius of the park.**

**Number of visits last year Number of families **

0 145

1 89

2 152

3 68

4 46

a. Show the probability distribution function of this random variable

b. What is the probability that a family visited the park exactly three times last year?

c. What is the probability that a family visited the park at least once last year?

d. What is the expected number of times a family visited the park last year? What is the interpretation of this value?

**3. 20% of the customers at XYZ Stores use a debit card to pay for their purchases. In a recent market research study, 20 of the Store's over 30,000 customers on record was randomly selected for two focus groups on new payment technologies.**

a. Is the selection of 20 customers a binomial experiment? Please explain.

b. What is the probability that 5 of the 20 customers selected use a debit card to pay for their purchases?

c. What is the probability that at least 4 of the 20 customers selected use a debit card to pay for their purchases?

d. What is the probability that at most 4 of the 20 customers selected use a debit card to pay for their purchases?

e. What is the probability that at least 3 but no more than 6 customers selected use a debit card to pay for their purchases?

**4. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes.**

- What is the expected number of calls in one hour?
- What is the probability that exactly two customers arriving at the drive-through lane in a nine-minute interval?
- What is the probability that less than two customers arrive at the drive-through lane a nine-minute interval?
- What is the probability that two or more customers arrive at the drive-through lane a nine-minute interval?