A can company reports that the number of breakdowns per 8-hour shift on its machine operated assembly line follows a Poisson distribution with a mean of 1.5.

1. What is the probability of exactly three breakdowns on the midnight shift?
2. What is the probability of greater than two breakdowns in one hour?
3. What is the probability that the time between two successive breakdowns is at most three hours?
4. If two hours have gone by without a breakdown, what is the probability that a breakdown will occur in the next one hour?

We have been using the same set of data (Data Set One) in the notes to illustrate production and costs. I have provided Data Set One in both tables below. When costs were calculated in the notes, fixed costs were $200. By using the term fixed costs economists are only referring to the fact that a firm must pay this expense no matter how much output it produces or sells. An example of a fixed cost could be the rent a small store pays on the space it rents. The rent will be the same for the duration of the lease, no matter if the store sells I item or 500 items. It is helpful to know what will happen to costs if the price of the variable or fixed resource changes.

Problem Two - Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the variable input (which is labor in this example) is not $50 but $55. I have created Table 2 for you to put your answers in. Assume that fixed costs remain at $230. When the price of a variable input changes which other costs will increase? Compare the costs you calculate for table two to the costs calculated in table one to find your answers.

TABLE TWO FOR ANSWERS TO PROBLEM TWO

Given vector s = [4, -5, 7], u = [-6, 8, 11], and v = [-5, 3, -7]
a. Let r1(t) be the vector equation through s and u. Express the vector equation r(t) in two ways and then find r(1); r(-5); r(9)
b. Let r2(t) be the vector equation through u and parallel to r1(t), Express r2(t) in two forms and then find r(-3); r(13); r(2)
c. Let w = 2s -4v, find r(t) through u and v

20 gtt/mL, 320 drops/minute = ______mL/min

a.70

b.24

c.16

d.144

15 gtt/mL, 300 drops/minute = ______mL/min

a. 20

b. 40

c.120

d. 32

A cat with a gastrotomy tube must receive 300 kcal daily. A 15-oz can of the prescribed diet has 1500 kcal. The prescribed diet must be diluted 50:50 with water to flow through the tube, and a maximum volume of 45 ml liquid can be given at one feeding. Approximately how many feedings does this cat need daily?

a. 10

b. 8

c. 4

d. 2

A patient with an esophagostomy tube must receive 200 kcal daily. A 12-oz can of the prescribed diet has 1200 kcal. The prescribed diet must be diluted 50:50 with water to flow through the tube, and a maximum volume of 30 ml liquid can be given at one feeding. Approximately how many feedings does this patient need daily?

a. 4

b. 3

c. 2

d. 6

4. Construct a frequency distribution, find the summary statistics (including the quartiles) for customer age, and graph by each type of customer (regular or promotion). Comment on the shape of the distribution for each type and discuss similarities or differences if any. (Think whether you should create an ungrouped or grouped frequency distribution.) Label the graphs completely.

5. Construct a box-and-whisker plot and find the summary statistics (including the quartiles) for net sales by each type of customer (regular or promotion). Make sure that you format the x-axes on each plot and compare the plots using the same scale. Comment on the shape of the distribution for each type and compare.

Why are some (not all) college graduates have a difficult time finding a job that is a good match with their skills (education)? Also, why are some college graduates paid less that other college graduates when they enter the labor market? How would you solve the above two problems if you were in charge.

11.You measure the weight of 37 turtles, and find they have a mean weight of 52 ounces. Assume the population standard deviation is 10.9 ounces. Based on this, what is the maximal margin of error associated with a 92% confidence interval for the true population mean turtle weight.
Give your answer as a decimal, to two places

12.In a survey, 18 people were asked how much they spent on their child's last birthday gift. The results were roughly shaped as a normal curve with a mean of $45 and standard deviation of $8. Find the margin of error at a 80% confidence level.

13. In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly shaped as a normal curve with a mean of $34 and standard deviation of $12. Construct a confidence interval at a 80% confidence level.

Give your answers to one decimal place.

.................. ± ..............

. There are ba (= 14) ways to arrange 1, 2, 3, ..., 8 in two rows of four so that (1) the integers increase in value as each row is read, from left to right, and (2) in any column the smaller integer is on top. Find, as in part (d) of Example 1.43, a) the arrangements that correspond to each of the fol- lowing. 1) 10110010 i) 11001010 lli) 11101000 b) the lists of four l's and four O's that correspond to each of these arrangements of 1, 2, 3, ...,8. 1) 1 345 ii) 1 2 37 fii) 1 2 4 5 2 6 7 8 4 5 6 8 3 6 7 8

Now, consider the following age-specific data:

1. Look at the age-specific rates in the table above. Compare the age-specific rates between the two populations? What do you conclude (1pt)?

2.Explain any difference in conclusion when comparing the crude and age-specific rates and discuss briefly the importance of considering age in this instance(2pts)