The builder of a new movie theater complex is trying to decide how many screens she wants. Below are her estimates of the number of patrons the complex will attract each year, depending on the number of screens available.

After paying the movie distributors and meeting all other noninterest expenses, the owner expects to net $2.5 per ticket sold. Construction costs are $1,000,000 per screen.

Instructions: Enter your responses as whole numbers.

a. Make a table showing the value of marginal product for each screen from the first through the fifth.

What property is illustrated by the behavior of marginal products?

• Diminishing returns to capital

• Increasing returns to capital

• Negative returns to capital

b. How many screens will be built if the real interest rate is 5.5 percent?

screen(s)


c. How many screens will be built if the real interest rate is 7.5 percent?

screen(s)


d. How many screens will be built if the real interest rate is 10 percent?

screen(s)

e. If the real interest rate is 5.5 percent, what is the highest construction cost per screen that would make a five-screen complex profitable?

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The builder of a new movie theater complex is trying to decide how many screens she wants. Below are her estimates of the number of patrons the complex will attract each year, depending on the number of screens available.

After paying the movie distributors and meeting all other noninterest expenses, the owner expects to net $2.5 per ticket sold. Construction costs are $1,000,000 per screen.

Instructions: Enter your responses as whole numbers.

a. Make a table showing the value of marginal product for each screen from the first through the fifth.

What property is illustrated by the behavior of marginal products?

• Diminishing returns to capital

• Increasing returns to capital

• Negative returns to capital

b. How many screens will be built if the real interest rate is 5.5 percent?

screen(s)


c. How many screens will be built if the real interest rate is 7.5 percent?

screen(s)


d. How many screens will be built if the real interest rate is 10 percent?

screen(s)

e. If the real interest rate is 5.5 percent, what is the highest construction cost per screen that would make a five-screen complex profitable?

SAT Score Analysis

You have been asked to analyze SAT scores (which may be 400 - 1600).  

You will be analyzing a population (a list) which consists of a number of

samples (lists) of student scores.

Here is the code to generate the  population/samples:

     import random

  population=[]

  for i in range(5):

  sample = []

  n = random.randint(5,10)

  for num in range(n):

  sample.append(random.randrange(400,1600))

  population.append(sample)  

The analysis should be conducted as follows:

  ##calculate the total number of scores  

  ##calculate the total value of all scores

  ##find the average score of the population  

  ##print the total number of scores  

  ##print the total value of all scores

  ##print the average of all of the scores

  ##while a sample has an average that is less than the

  ##average of all scores add a random value 1000 - 1600

  ##to the sample until the average is no longer less than

  ##the average of all scores

  ##please note: this could result in lots of numbers

  ##being appended to the sample

  ##print the population

  ##adjust the population by

  ##removing the highest and lowest scores from each sample

  ##print the (adjusted) population  

  ##calculate the total number of (adjusted) scores  

  ##calculate the total value of all (adjusted) scores

  ##find the average score of the (adjusted) population  

  ##print the total number of (adjusted) scores  

  ##print the total value of all (adjusted) scores

  ##print the average of all of the (adjusted) scores

Done in Python Format please

Please show work:

Minnesota Financial is a subsidiary of Mayberry Enterprises. Processing loan applications is the main task of the corporation. They charge a $500 fee for every loan application processed. Next year's fixed costs have been projected as follows: sales and advertising $40,000; building rental, $18,000; Depreciation of computers and office equipment $27,000; and other fixed costs, $5,000. The projected variable costs include: loan officer’s wages, $27 per hour (a loan application takes 5 hours to process); supplies $16.40 per application; and other variable costs, $8.60 per application. (Round all answers to the closest full number)

Questions:

1. Determine the number of loan applications the company must process to (a) break even and (b) earn a profit of $50,000 (round to the closest full number).

2. Determine the number of loan applications the company must process to earn a target profit of $50,000 if fixed costs increase by $10,000.

3. Assuming the original fixed cost information and assuming that 500 loan applications are processed, compute the loan application fee the company must charge if the target profit is $75,000.

4. If 750 loan applications is the maximum number her staff can handle. How much more (less) can be spent on promotional costs if the highest fee tolerable to the customer is $600, if variable costs cannot be reduced, and if the target net income for such an application load is $100,000?

1. Find the probability that x is between four and 10. (Round your answer to four decimal places.)

X ~ N(5, 3)

2. Suppose

X ~ N(−1, 4).

What is the z-score of  x = 10?  (Enter an exact number as an integer, fraction, or decimal.)
z =

3. The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories.

Find the probability that the percent of fat calories a person consumes is more than 43. (Round your answer to four decimal places.)

4. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 230 feet and a standard deviation of 46 feet. Let X = distance in feet for a fly ball.

Give the distribution of X.
X ~ ( , )

5. The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts.

Find the probability that a CD player will last between 2.8 and eight years.

(b) Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.)

P( < x <   ) =  

At the entrance of Walmart, there is a greeter named Mary who says “Have a nice day” to the customers as they leave the store after shopping. The probability that a customer responds to Mary is 70%. For each of the following scenarios related to Mary the greeter--state the following (note: R.V. means random variable) (1) Define the R.V.--- that means something like, “Let X be the number of people who…..” (2) Define the distribution and parameter(s) of the R.V. (3) Give the support of the R.V. (4) Write the probability statement

a) Sophie leaves Walmart and Mary says “Have a nice day”. Find the probability that Sophie does not respond to Mary.

b) A family of 5 leaves Walmart after shopping, find the probability that 2 of the family members respond to Mary. Assume that each person’s response is independent.

c) Mary just started her work shift at Walmart. She has said “have a nice day” to 3 people and received no response. What is the probability that it will take more than 5 people total for Mary to get her first response?

d) What is the probability that Mary will get her 4th response, from the 7th person who walks out?

e) The store manager knows that after 5 pm, on average there are 20 customers leaving the store every 30 minutes. What is the probability that 5 customers leave Walmart between 6:10 and 6:20 pm?

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in table #4.3.3 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Table #4.3.3: Dolphin Activity Activity Period Morning Noon Afternoon Evening Total Travel 6 6 14 13 39 Feed 28 4 0 56 88 Social 38 5 9 10 62 Total 72 15 23 79 189 a.) What is the probability that a dolphin group is partaking in travel? b.) What is the probability that a dolphin group is around in the morning? c.) What is the probability that a dolphin group is partaking in travel given that it is morning? d.) What is the probability that a dolphin group is around in the morning given that it is partaking in socializing? e.) What is the probability that a dolphin group is around in the afternoon given that it is partaking in feeding? f.) What is the probability that a dolphin group is around in the afternoon and is partaking in feeding? g.) What is the probability that a dolphin group is around in the afternoon or is partaking in feeding? h.) Are the events dolphin group around in the afternoon and dolphin group feeding mutually exclusive events? Why or why not? i.) Are the events dolphin group around in the morning and dolphin group partaking in travel independent events? Why or why not?

A village has six residents, each of whom has accumulated savings of $100. Each villager can use this money either to buy a government bond that pays 14 percent interest per year or to buy a year-old llama, send it onto the commons to graze, and sell it after 1 year. The price the villager gets for the 2-year-old llama depends on the quality of the fleece it grows while grazing on the commons. That, in turn, depends on the animal’s access to grazing, which depends on the number of llamas sent to the commons, as shown in the following table:

The villagers make their investment decisions one after another, and their decisions are public.

a. If each villager decides individually how to invest, how many llamas will be sent onto the commons, and what will be the resulting village income?

Number of llamas:_

Instructions: Enter your response as a whole number.

Village income: $_

b. What is the socially optimal number of llamas for this village?

Socially optimal number of llamas:_

What would village income be if the socially optimal number of llamas were sent onto the commons?

Instructions: Enter your response as a whole number.

Village income: $_

c. The village committee votes to auction the right to graze llamas on the commons to the highest bidder. Assuming villagers can both borrow and lend at 14 percent annual interest, how much will the right sell for at auction?

Instructions: Enter your response rounded to two decimal places.

$_

What will be the resulting village income?

Instructions: Enter your response as a whole number.

Village income: $_

In Washington state, 68.2% of adults visit the dentist for their recommended twice-yearly cleanings. Let X be the random variable that counts the number of adults in a group of 5 people who have visited the dentist for their recommended twice-yearly cleanings.

(a) In the group of 5 people, find P(X=3), or the probability that exactly 3 in the group of 5 have visited the dentist for their twice-yearly cleaning. (round to 4 decimal places)

(b) In the group of 5 people, find the probability that at least 3 in the group of 5 have visited the dentist for their twice-yearly cleaning. (round to 4 decimal places)

(c) In the group of 5 people, find the probability that no more than 3 in the group of 5 have visited the dentist for their twice-yearly cleaning. (round to 4 decimal places)

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.902 g and a standard deviation of 0.287 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 33 cigarettes with a mean nicotine amount of 0.832 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 33 cigarettes with a mean of 0.832 g or less.
P(x-bar < 0.832 g) =  
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.