Question 1
A small manufacturing company recently instituted Six Sigma training for its employees. Two
methods of training were offered: online and traditional classroom. Management was interested
in whether the division in which employees worked affected their choice of method.

Below is a table summarizing the data.

(a) What is the probability that an employee chose online training? [2 marks]
(b) What is the probability that an employee is in the quality division and chose online training?
[2 marks]
(c) What is the probability that an employee chose online training given that he or she is in the
sales division? [2 marks]
(d) What is the probability that an employee chose online training or is from the sales division?
[3 marks]
(e) Are the events “chose online training” and “from the sales division” independent? Give
reason for your answer. [2 marks]

Question 2
A game consists of flipping a fair coin twice and counting the number of heads that appear. The
distribution for the number of heads, X, is given by: P(X = 0) = ¼; P(X =1) =1/2; P(X = 2) =¼

A player receives $0 for no heads, $2 for 1 head, and $5 for 2 heads (there is no cost to play the
game). Calculate the expected amount of winnings ($). [2 marks]

Question 3
Internet service providers (ISP) need to resolve customer problems as quickly as possible. For
one ISP, past data indicate that the likelihood is 0.80 that customer calls regarding Internet
service interruptions are resolved within one hour. Out of the next 10 customer calls about
interrupted service,
(a) What is the probability that at least 7 will be resolved within one hour? [4 marks]
(b) How many customers would be expected to have their service problems resolved within one
hour? [1 mark]

Question 4
A mail-order company receives an average of five orders per 500 solicitations. If it sends out 100
advertisements, find the probability of receiving at least two orders. [Hint: Use the Poisson
distribution]. Ensure that you define the variable of interest.

Question 5
An airline knows from experience that the distribution of the number of suitcases that get lost
each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the
probability that during a given week the airline will lose between 10 and 20 suitcases?

Question 6
Assume that the heights of women are normally distributed with a mean of 62.2 inches and a
standard deviation of 2.3 inches. Find the third quartile that separates the bottom 75% from the
top 25%. Total 4 marks

The beer store sells potato chips and has does so for a long time. Over the last four years, it has observed that its weekly demand for potato chips varies quite a bit from week to week, but does not follow any seasonal or predictable pattern. The volume of potato chips is much higher than beer, and the store estimates that weekly demand can be modeled as being normally distributed with a mean of 35 bags per week, and a standard deviation of 7.

Assume that the store has a given amount of inventory at the start of a week, and has no opportunity to replenish this inventory during the week. In particular for each of the question we’ll assume that the store has 34 bags of inventory at the start of the week.

Part A:

1. Based on the assumed normal distribution for demand, what is the probability that weekly demand is less than or equal to 30 bags? (rounded to three decimal places)

2. What is the probability that weekly demand exceeds 45 bags? (rounded to three decimal places)

Part B

1. What is the probability that it will sell all 34 bags? (rounded to three decimal places)

2. What is the probability that it has at least 2 bags of chips leftover at the end of the week? (rounded to three decimal places)

3. What is the probability that unmet demand equals or exceeds 3 bags? (rounded to three decimal places)

4. What is the expected number of bags that the store will sell? (rounded to three decimal places)

5. What is the expected number of bags in inventory at the end of the week? (rounded to three decimal places)

6. What is the expected unmet demand? (rounded to three decimal places)

Which has the highest normal freezing point?
N₂
H₂
CH₄
Which has the greatest heat of vaporization?
H₂O
H₂S
H₂Se
H₂Te
Which has the highest normal boiling point?
H₂O
NH₃
CH₄
Which has the greatest viscosity?
CH₃(CH₂)₃CH₃
HOCH₂CH₂OH
CH₃CH₂OH
Which has the smallest enthalpy of fusion?
Li₂O
MgO
HCl
H₂O

A second-price sealed-bid auction is an auction in which every bidder submits his or her bid to the auctioneer, the auctioneer announces the winner to be the bidder who submits the highest bid, and the winner pays the highest bid among the losers. Is the following statement True, False, or Uncertain? Explain why. Every player has a weakly dominant strategy in second-price auction.

Using Matlab, create a code that determines the highest real root of f(x)=x3-6x2+11x-6.1 using the Newton-Raphson method with x0=3.5 for three iterations. Verify that the process is quadratically convergent.

I found the code to get the highest real root (root for three iterations = 3.0473), however, I do not know how to verify that it is quadratically convergent.

the number of fire engines available to extinguish fires in a small town is two. When a fire occurs it occupies one fire engine for a full day. If the occurence of fires is Poisson distributed with a mean of 0.7 per day, what is the probability that a fire will occur for which no engine is available?

A basketball player makes 60% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he throws 4 shots. Let X = the number of shots that he makes. What is the probability that he makes 1 shot?

A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 3 shots. Let X = the number of shots that he makes. What is the probability that she makes 2 shots?

A basketball player makes 60% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he takes 4 shots. Let X = the number of shots that he makes. What is the probability that he makes 3 shots?