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1.

For the Week 2 Complete assignment, solve each problem and answer each question that

corresponds with it. Explain how you arrived at the answer for each problem. The total word

count for your assignment should be a minimum of 1200 words.

Identify which of the following values are valid and not valid numbers for a probability:

a. 2.1

b. 4/4

c. 76%

d. 0.8

e. 9/8

f. 110%

g. –1/3

h. 1

i. 0.007

2.

Consider the experiment of rolling two dice.

a. What is the probability of obtaining a sum of eight?

b. What is the probability of obtaining a sum of eight or less?

c. What is the probability of obtaining a sum of four or more?

3.

A survey was conducted in which 150 households were asked how many working televisions

they owned. The results are as follows:

a. What is the probability that a randomly selected household has one television?

b. What is the probability that a randomly selected household has more than two televisions?

c. What is the probability that a randomly selected household has fewer than four

televisions?

d. Is this an example of classical, empirical, or subjective probability?

4.

The following table indicates the frequency of lap-tops sold per day at a local Best Buy store

during a particular time period. During the period, there were never any days in which more than

seven lap-tops were sold.

a. What is the probability that three laptops will be sold tomorrow?

b. What is the probability that four or more laptops will be sold tomorrow?

c. What is the probability that either one or two laptops will be sold tomorrow?

d. What is the probability that fewer than two lap-tops will be sold tomorrow?

e. Is this an example of classical, empirical, or subjective probability?

5.

Consider the following experiment—a card is cho-sen randomly from a 52-card deck, observed,

and then replaced. After shuffling the deck, a second card is drawn and observed. Consider the

following events:

A = The first card is the jack of diamonds

B = The second card is the jack of diamonds

a. Are these two events mutually exclusive?

b. Are these two events independent?

6.

A local university has a student population that is 57% male. Sixty-four percent of the students

are undergraduates; 40% are both male and undergraduates.

a. What is the probability that a randomly selected student is both female and an

undergraduate?

b. What is the probability that a randomly selected student is either male or an

undergraduate?

7.

A call center for customer support records the time each customer requires for service and

whether the call occurred during the week (Monday through Friday) or during the weekend

(Saturday and Sunday). The results are shown in the following table:

Determine the probability that a randomly selected call

a. was during the week.

b. was less than 20 minutes.

c. was 10 to less than 20 minutes.

d. was more than 20 minutes during the weekend.

e. was 15 to less than 20 minutes or occurred during the weekend.

f. was 5 to less than 10 minutes, given it occurred during the week.

g. occurred during the week, given it was 5 to less than 10 minutes.

h. Construct a decision tree for these events.

8.

AIG, an international insurance and financial services organization, recently announced that the

performance of employees would be rated on a scale from 1 to 4. The top 10% of employees

would receive a 1 rating, 20% of the employees would be rated with a 2, and 50% would be

rated with a 3. The remaining employees would receive a 4 rating. The rating scheme is known

as a forced-ranking system. It was begun after the government bailed out AIG and forced the

company to link compensation to performance. Suppose the Wilmington, Delaware, facility of

AIG has 450 employees. Determine the number of employees who can receive each rating.

9.

Tees R Us, which manufactures and sells T-shirts for sporting events, is providing shirts for an

Tees R Us, which manufactures and sells T-shirts for sporting events, is providing shirts for an

upcoming tournament. Each shirt will cost $10 to produce and will be sold for $16. Any unsold

shirts at the end of the tournament can be sold for $5 apiece in the near future. Tees R Us

assumes the demand for the shirts will be 1,000, 2,000, 3,000, or 4,000. The company also

estimates that the probabilities of each of these sales levels occurring will be 15%, 25%, 30%,

and 30%, respectively. Determine the expected monetary value of the project if Tees R Us

chooses to print 3,000 shirts for the tournament.