5. The Gardner Theater, a community playhouse, needs to determine the lowest-cost production budget for an upcoming show. Specifically, they have to determine which set pieces to construct and which, if any, set pieces to rent from another local theater at a predetermined fee. However, the organization has only two weeks to fully construct the set before the play goes into technical rehearsals. The theater has two part-time carpenters who work up to 12 hours a week, each at $10 an hour. Additionally, the theater has a part-time scenic artist who can work 15 hours per week to paint the set and props as needed at a rate of $15 per hour. The set design requires 20 flats (walls), two hanging drops with painted scenery, and three large wooden tables (props). The number of hours required for each piece for carpentry and painting is shown below:

Flats, hanging drops, and props can also be rented at a cost of $75, $500, and $350 each, respectively. How many of each unit should be built by the theater and how many should be rented to minimize total costs?

Table below shows the multiple logistic regression for factors associated with having three or more cardiovascular disease risk factors among a population of 500 participants who participated in a cross-sectional survey.

Table 4. Multiple Logistic Regression for the predictors of having three or more Cardio Vascular Disease risk factors (N=500)

Which variable(s) is considered to be statistically significant? Interpret the odds ratio and the 95% confidence interval for the significant variable(s). [PROVIDE JUSTIFICATION(S) AND RATIONALES]

Bob Sparrow purchases steak from a local meatpacking house. The meat is purchased on Monday at $2.00 per pound, and the shop sells the steak for $3.00 per pound. Any steak left over at the end of the week is sold to a local zoo for $0.50 per pound. The possible demands for steak and the probability of each are shown in the following table:

Demand (lbs.) Probability

20 0.2

21 0.3

22 0.5

Bob must decide how much steak to order in a week. Bob wants to maximize expected value. What is his expected value when purchasing optimally? [Hint: construct a payoff table for each of his decisions and each state of nature.] A) 20 B) 20.5 C) 20.25 D) 21 9.

What is Bob Sparrow’s Expected Value of Perfect Information? A) 20.5 B) 1.3 C) 0.8 D) 1.05

A)

A student stretches an elastic band by 0.8 m in 0.5 seconds. The spring constant of the elastic band is 40 N/m. What was the power exerted by the student?

B)

A student pushes a 0.2 kg box against a spring causing the spring to compress 0.15 m. When the spring is released, it will launch the box vertically into the air. What is the maximum height the box will reach if the spring constant is 300 N/m?

C)

A student connects a 1 hp motor to a bicycle. How much time will it take for the bicycle to accelerate from rest to a speed of 5.0 m/s if the combined mass of the student and the bicycle is 120 kg? (1 hp = 746 W)

The following table summarizes the responses of a sample of 25 workers who were asked how many miles they had to travel to go to work.

Suppose you build a histogram with this information. Describe it

A. "A single peak, skewed to the left (left-skewed)."

B. "A single peak, skewed to the right (right-skewed)."

C. "Bimodal, skewed to the right (right-skewed)."

D. "Bimodal, skewed to the left (left-skewed)."

"The survival time of patients after a certain type of surgery has a skewed distribution to the right due to the presence of outliers. Consequently, which statement is more likely to be correct?"

A. Median (median)> range

B. Average (mean) <median (median)

C. Average (mean)> median (median)

D. None of the above.

A distribution will be skewed to the left (left-skewed) if

A. Median <mid axis (midhinge)

B. Medium> mid axis (midhinge)

C. Median = mid axis (midhinge)

D. None of the above.

"Since P (A) = 0.4, P (B) = 0.5 and P (A ∩B) = 0.05. Then:"

A. P (A∪B) = 0.80; P (A / B) = 0.1

B. P (A∪B) = 0.85; P (A / B) = 0.15

C. P (A∪B) = 0.85; P (A / B) = 0.10

D. None of the above.

The average of the exam of a class of 30 students was 75. The average of the exam for the 20 male students of that class was 70. Then the average of the exam for the 10 female students was:

A. 85

B. 80

C. 75

D. None of the above.

"Two events are complementary (that is, they are complements), yes"

A. The sum of your odds is equal to one.

B. The probability of your interception is equal to one.

C. They are two independent events with equal probabilities.

D. None of the above.

What probability function can be used to describe the number of damaged printers in a random sample of 12 printers taken from a shipment of 70 printers consisting of 6 damaged printers?

A. Poisson

B. Hypergeometric

C. Binomial

D. None of the above.

You have the following probability distribution of the random variable X:

The expected value of X is:

A. 175

B. 150

C. 205

D. None of the above.

The variable Z has a standard normal distribution. The probability P (0.71 <Z <1.43) is:

A. 0.1625

B. 0.92

C. 0.5

D. 0.485

"Suppose that X has a normal distribution with a mean μ = $ 64. Given that P (X> $ 75) = 0.2981, we can calculate that the standard deviation of X is approximately"

A. $ 20.75

B. $ 13.75

C. $ 5.83

D. $ 7.05

"In Quebec, 90% of the population is Catholic. In a random sample of 8 people find the probability that the sample contains at least five Catholics."

A. 0.005

B. 0.0331

C. 0.995

D. 0.9619

Problem 3: Food Prices: Target versus Safeway.  Grocery prices of the same randomly selected items were collected and compared from Target and Safeway.  Imagine you were interested in conducting a hypothesis test to determine whether the mean prices were significantly different.  Note: to answer the questions below, subtract Target price – Safeway price (i.e. subtract Safeway price from Target price).

Data:

Mean = -0.5071, Standard Deviation = 0.9012

1. Construct a 95% confidence interval using the above data.  Please do this “by hand” using the formula and showing your work (please type your work).  Use your t-table (found in the last page of our formula packet) to obtain your t* critical value needed for the confidence interval.  Present this confidence as (lower limit, upper limit).

3. Imagine you were using a hypothesis test to determine if a significant difference exists in mean price between the two stores (the hypotheses would be H₀: m_D= 0 vs H_a: m_D≠0).  What conclusion can be made in this case using only your confidence interval? Provide an answer and a reason for your choice in one or two sentences.  Again, please only use your confidence interval to answer this question (i.e. do not run this hypothesis test).

1. Complete Table 1 by calculating the volume of 2.0 mg/mL myoglobin, 6.0 M GuHCl, and 0.5 M phosphate buffer needed to make the 15 solutions needed for the experiment.

Create a matlab function that converts Miles per hour to feet per second. Please show code in matlab

Magna Magna Corporation uses trucks to transport bottles from the warehouse to different retail outlets. Gasoline costs are $ 0.26 $0.26 per mile driven. Insurance costs are $ 7 comma 000 $7,000 per year. Calculate the total costs and the cost per mile for gasoline and insurance if the truck is driven​ (a) 16 comma 000 16,000 miles per year or​ (b) 35 comma 000 35,000 miles per year. ​(Round the cost per mile answers to the nearest​ cent, $X.XX.)

in a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home. Use .05 significance level to test the claim that more than 50% of car crashes occur within 5 miles of home.

Step 1: Ho:___ Ha:_____

Step 2: significance level a= .05

step 3 : Test :___

VALUES FOR EACH REQUIRED ENTRY ON CALCULATOR

p-value:____

Step 4: Decision

Reason:

Conclusion:

Please include numbers to put into the calculator and what test you use