The executive education (EE) unit at the Business School of Central State University offers both open-enrollment (anyone can sign up) and custom (designed for a specific client) executive education programs. CSU has just received an inquiry from a prospective client about its prices for leadership seminars. The prospective client wants bids for three alternative activity levels: (1) one seminar with 20 participants, (2) four seminars with 20 participants each (80 participants total), or (3) eight seminars with 140 participants in total. EE’s cost analyst has provided the following differential cost estimates.

In addition to the preceding differential costs, EE allocates fixed costs to jobs on a direct-labor-cost basis, at a rate of 75 percent of direct labor costs (excluding setup costs). For example, if direct labor costs are $100, EE would also charge the job $75 for fixed costs. EE charges clients for its costs plus 25 percent. For the purpose of charging customers, costs equal the setup costs plus materials costs plus differential labor costs plus allocated fixed costs. EE has enough excess capacity to handle this job with ease.

Required:

a. Assume EE's bid equals the total cost, including fixed costs allocated to the job, plus the 25 percent markup on cost. What should EE bid for each of the three levels of activity?

b. Compute the differential cost (including setup costs) and the contribution to profit for each of the three levels of activity. Note that fixed costs are not differential costs.

c. Assume the prospective client gives three options. It is willing to accept either of EE's bids for the one-seminar or four-seminar activity levels, but the prospective client will pay only 85 percent of the bid price for the eight-seminar package. EE's director responds, "We can't make money in this business by shaving our bids! Let's take the four-seminar option because we make the most profit on it."

c-1. What would be the contribution to profit for each of the three options?

c-2. Do you agree with the EE's director?

The executive education (EE) unit at the Business School of Central State University offers both open-enrollment (anyone can sign up) and custom (designed for a specific client) executive education programs. CSU has just received an inquiry from a prospective client about its prices for leadership seminars. The prospective client wants bids for three alternative activity levels: (1) one seminar with 20 participants, (2) four seminars with 20 participants each (80 participants total), or (3) eight seminars with 140 participants in total. EE’s cost analyst has provided the following differential cost estimates:

In addition to the preceding differential costs, EE allocates fixed costs to jobs on a direct-labor-cost basis, at a rate of 75 percent of direct labor costs (excluding setup costs). For example, if direct labor costs are $100, EE would also charge the job $75 for fixed costs. EE charges clients for its costs plus 20 percent. For the purpose of charging customers, costs equal the setup costs plus materials costs plus differential labor costs plus allocated fixed costs. EE has enough excess capacity to handle this job with ease.

Required:

a. Assume EE's bid equals the total cost, including fixed costs allocated to the job, plus the 20 percent markup on cost. What should EE bid for each of the three levels of activity?

b. Compute the differential cost (including setup costs) and the contribution to profit for each of the three levels of activity. Note that fixed costs are not differential costs.

c. Assume the prospective client gives three options. It is willing to accept either of EE's bids for the one-seminar or four-seminar activity levels, but the prospective client will pay only 85 percent of the bid price for the eight-seminar package. EE's director responds, "We can't make money in this business by shaving our bids! Let's take the four-seminar option because we make the most profit on it."

c-1. What would be the contribution to profit for each of the three options?

c-2. Do you agree with the EE's director?

9. Discrete probability distributions #1

A study conducted by three law school professors found that asylum seekers in the United States face broad disparities in the nation’s immigration courts. The professors discovered that 54% of refugees who ask for asylum in the San Francisco immigration court win asylum, but only 12% are granted asylum in the Atlanta immigration court. [Source: Julia Preston, “Wide Disparities Found in Judging of Asylum Cases,” The New York Times, May 31, 2007.]

Select the appropriate distribution in the Distributions tool to help answer the questions that follow.

0123BinomialPoisson

Select a Distribution

You randomly select 20 refugees who are asking for asylum in the San Francisco immigration court. Let X denote the number of asylum seekers who win their cases.

The probability that exactly 11 asylum seekers are granted asylum is   .

The probability that at least seven asylum seekers are granted asylum is   .

The expected value of X is   , and the standard deviation of X is

10. Discrete probability distributions #2

The Geminids is an annual meteor shower that appears every December. Under a clear, dark sky, an observer of the Geminids would see an average of 20 meteors per 10-minute period (if the meteors’ emanation point were directly overhead).

Select the appropriate distribution in the tool to help answer the following questions. (Note: You will need to read the questions first to determine the appropriate distribution.)

0123BinomialPoisson

Select a Distribution

It’s December and you host a Geminids party on the peak night of the meteor shower. The sky is clear and dark, and the meteors’ emanation point is directly overhead. You and your friends watch the sky for 10 minutes. The probability that you see exactly 20 meteors is0.0888   .

The probability that you see more than 16 meteors while watching the night sky for 10 minutes is   .

Select the appropriate distribution in the tool below to help answer the following questions. (Note: You will need to read the questions first to determine the appropriate distribution.)

0123BinomialPoisson

Select a Distribution

After going inside for a midnight snack, you and your friends go back outdoors for a 25-minute sky-gazing session. The probability that you observe no more than 48 meteors during this sky-gazing session is   .

The number of meteor sightings over 20 minutes has an expected value of    and a standard deviation of   

Question 5 options: A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds that 77% of them received a passing grade. Create a 99% confidence interval for the population proportion of passing test scores. Enter the lower and upper bounds for the interval in the following boxes, respectively. You may answer using decimals rounded to four places or a percentage rounded to two. Make sure to use a percent sign if you answer using a percentage.

Question 6 options: An online retailer wants to estimate the number of visitors that click on their advertisement from a particular website. Of 978 page views in a day, 8% of the users clicked on the advertisement. Create a 90% confidence interval for the population proportion of visitors that click on the advertisement. Enter the lower and upper bounds for the interval in the following boxes, respectively. You may answer using decimals rounded to four places or a percentage rounded to two. Make sure to use a percent sign if you answer using a percentage.

Twenty-seven high-school seniors decided to take part in an investigation of the special “exam preparation” books that purportedly help one get ready for college entrance examinations. The group divided itself into three groups on a purely random basis. Two of the groups used the books, each group selecting a different book. The third group did not use the books. Listed below are the obtained entrance exam scores. Perform the ANOVA using the 5% level of significance and interpret your results.

BOOK I: 532 455 440 620 560 522 517 520 510

BOOK II: 540 570 520 620 660 605 602 590

NO BOOK: 380 470 441 487 420 390 450 510 430 560

Twenty-seven high-school seniors decided to take part in an investigation of the special “exam preparation” books that purportedly help one get ready for college entrance examinations. The group divided itself into three groups on a purely random basis. Two of the groups used the books, each group selecting a different book. The third group did not use the books. Listed below are the obtained entrance exam scores. Perform the ANOVA using the 5% level of significance and interpret your results.

BOOK I: 532 455 440 620 560 522 517 520 510

BOOK II: 540 570 520 620 660 605 602 590

NO BOOK: 380 470 441 487 420 390 450 510 430 560

In a certain region, 20% of people over age 50 didn't graduate from high school. We would like to know if this percentage is the same among the 25-30 year age group. Use critical values to exactly 3 decimal places.

(a) How many 25-30 year old people should be surveyed in order to estimate the proportion of non-grads to within 7% with 95% confidence?

(b) Suppose we wanted to cut the margin of error to 4%. How many people should be sampled now?

(c) What sample size is required for a margin of error of 5%?

Every teacher at a high school is given a n-digit code, e.g. 530...297 (n digits in total).

(1) How many different codes are there?

(2) How many codes read the same backward and forward? (Consider the cases where n is odd or even.)

(3) How many codes contain odd digits only?

(4) How many codes contain at least one even digit?

(5) Consider the case where n is 6. How many codes have distinct digits? (That is, no digit appears more than once.)

In Study Design 2, Super Sneaker Company drew at random two groups of 12 high school students from the Halifax school district database. After obtaining their shoe sizes, the company manufactured 12 pairs of shoes for group 1, each pair with both soles constructed from material A, and 12 pairs of shoes for group 2, each pair with both soles constructed from material B. After 3 months, the amount of sole wear in each shoe was recorded in standardized units, as in the first design.

Using option III, the following data were used to test the hypothesis that wear for material B was greater than wear for material A.

Assume the standard deviation of wear is the same for both materials A and B. Calculate the test statistic. Use at least 5 digits to the right of the decimal.  [3 pt(s)]

Is this a 1-sided or a 2-sided test?
2-sided
1-sided
[1 pt(s)]

Which interval in the table contains the p-value for the test?
p-value ≤ 0.005
0.005 < p-value ≤ 0.01
0.01 < p-value ≤ 0.025
0.025 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
p-value > 0.1
[3 pt(s)]

What is the 90% confidence interval for the difference in wear between material B and material A (μ_B − μ_A)? Use software to get a more precise critical value, but confirm it's roughtly the same value you get from the table.  Use at least 5 digits to the right of the decimal. Lower bound: ___ Upper bound: ___