QMS 102 - Exam Review 1.

The Westminster Hotel Restaurant summarized its December 12th restaurant data by constructing the cross classification table of entree, beverage and dessert choices below. BEVERAGE> DESSERT> E N T R E E

a. b. c.

Beer

Wine

Coffee

Pie

Cake

Ice Cream

Pie

Cake

Ice Cream

Pie

Cake

Ice Cream

Beef

3

1

2

0

0

0

2

0

3

Chicken

4

4

0

3

0

5

0

0

0

Fish

0

2

0

2

0

1

5

3

0

Use the table above as a basis for assigning probabilities for the following questions. What is the probability that a customer’s entree will be fish? If a customers entree is not beef, what is the probability that the customer will have pie for desert? What is the probability that the customer will have pie or chicken?

2.

Every month the Westminister Hotel constructs a histogram of daily room rentals. The management is concerned that the number of rooms rented per day in December 1998 is below that of the previous month and has constructed a histogram based on the first 15 days of December.

a.

Using information available from the histograms, determine if the average number of rooms rented per day in December (so far), is less than in November.

b.

Is the relative variability in the number of rooms rented per day in December (so far), more than that of November?

3.

After midnight on weekdays, room service calls are randomly and independently received at the front desk at the rate of 0.3 calls per hour. The management of the Westminster Hotel is also aware that 40% of room service calls are a request for a pizza.

a.

Next Tuesday, what is the probability that no room service calls will be made between 1am and 2am.

b.

Next Wednesday, what is the probability that more than 3 room service calls will be received between 1am and 3am?

c.

Suppose that between 2am and 5am tonight that there were 6 service calls. What is the probability that at most 3 pizzas were ordered in that period?

4.

To develop an efficient marketing strategy the Westminster Hotel wanted to understand the origin (home city) of its customers. The results of a survey of 2000 previous guests of the Westminster Hotel was summarized on the pie chart- “Origin of Customers”.

a.

The management wants to know why their guests choose the Westminster Hotel and randomly selected 12 of its current customers for an additional survey. What is the probability that at least 2 of the 12 are from Toronto?

b.

The management is considering randomly selecting 100 guests sampled in the survey of previous customers and sending them a discount coupon. What is the probability that less than 20% of the sample of 100 guests will be from Toronto?

5.

The management of the Westminster Hotel wants to better understand its guests. A key factor is the guest’s annual incomes in dollars. The hotel has managed to obtain small but random samples from each of the most recent 3 years. An analysis is given below. Assume that inflation has been negligible over the three years.

a.

What is the total income of those customers in the 1997 sample?

b.

The means of the incomes have been increasing over the 3 years. Can the management therefore conclude that it is attracting customers with higher incomes as time passes?

c.

What is the value for the “right fence” used in the construction of the Box-Whisker diagram of 1998 incomes?

Analysis of annual incomes for customers of the Westminster Hotel Small samples from 1996, 1997 and 1998 INC96 INC97 INC98 N Valid 30 30 32 Missing 2 2 0 Mean 50756.8 50876.6 51456.6 Std. Deviation 15574.7 20626.3 23993.6 Percentiles 25 39929.1 37912.1 34291.2 50 49915.1 47538.5 43532.2 75 60040.9 57749.5 57998.7

6.

Check out times at the Westminster Hotel are normally distributed with a mean of 9:45 am (585 minutes after midnight) and a standard deviation of 30 minutes.

a.

What proportion of Westminster Hotel customers check out after the standard checkout time of 11am (more than 660 minutes after midnight)?

b.

What is the 70th percentile of checkout times?

c.

The hotel usually assigns extra staff to the checkout counter if it expects more than 25 customers will be checking out between 9am and 10am. If there are 80 guests staying at the hotel tonight, will the hotel need to assign extra staff to the checkout counter tomorrow morning?

7.

(Mark distribution 5 )

The management is concerned about the length of time it takes to prepare a room for the next guest and has recorded the times taken over a large number of different days, rooms and cleaning staff. The hotel plans to continuously monitor the room preparation process by randomly selecting the preparation times of 4 different room each day and computing the sample mean. How often will the daily sample mean exceed 16.5 minutes in January 1999, if there is no underlying change to the room preparation process?

8.

Cross out the LETTER of the answer which is correct

1.

Every 10th guest at the Westminster Hotel is asked to fill out a satisfaction survey. This type of sampling is a. Cluster sampling b. Systematic sampling c. Stratified sampling d. Simple random sampling e. Quota Sampling

2.

What is the largest possible raw data value in the frequency distribution class "20.0 and less than 30.0". a. 29.0 b. 29.5 c. 29.9 d. 30.0 e. None of the above

3.

The data value "2000" referring to a year, is an example of what measurement scale? a. Ordinal b. Interval c. Ratio d. Nominal e. Millennium

4.

If the smallest value in a data set is decreased substantially, which measure of variability will be the least affected? a. Interquartile Range b. Variance c. Standard Deviation d. Range e. Coefficient of Variation