Jon Hoke owns a bicycle shop. He stocks three types of bicycles: road-racing, cross-country

and mountain. A road-racing bike costs $1,200, a cross-country bike costs $1,700 and a

mountain bike costs $900. He sells road-racing bikes for $1,800, cross-country bikes for $2,100

and mountain bikes for $1,200. He has $12,000 available this month to purchase bikes. Each

bike must be assembled: a road-racing bike requires 8 hours to assemble, a cross-country bike

requires 12 hours and a mountain bike requires 16 hours. He estimates that he and his

employees have 120 hours available to assemble bikes. He has enough space in his store to

order 20 bikes this month. Based on past sales, John wants to stock at least twice as many

mountain bikes as the other two combined because mountain bikes sell better. Formulate

(develop the objective function and constraints) a linear programming model for this problem

where the Jon’s objective is to maximize total profits. Generate the solution using Excel Solver.

Please include Solver explanation. (step by step)

Standard deviation is a useful concept in performance management. Let us say that a director in a local fire department wants to know any variation between the performance of this year and that of the last year. He draws a sample of 10 response times of this year ( in minutes): 3.0, 12.0, 7.0, 4.0, 4.0, 6.0, 3.0, 9.0, 11.0, and 15.0, comparing them with a sample of 10 response times last year ( in minutes): 8.0, 7.0, 8.0, 6.0, 6.0, 9.0, 7.0, 9.0, 8.0, and 6.0.

a. Does he see a performance variation by the mean? ( 10 points)

b. Does he see a performance variation by the standard deviation? If he does, is it performance improvement or deterioration from the last year? Why? ( 10 points)

c. Now, imagine that your are a citizen receiving fire protection services from the local fire department. How do you evaluate the response times of the fire department, by the mean, by the standard deviation, or by both? Please explain

A random variable is normally distributed with a mean of 24 and a standard deviation of 6. If an observation is randomly selected from the​ distribution,

a. What value will be exceeded 5​% of the​ time?

b. What value will be exceeded 90% of the​ time?

c. Determine two values of which the smaller has 20% of the values below it and the larger has 20​% of the values above it.

d. What value will 10​% of the observations be​ below?

find z0.48

Assume the following data represent the cost of a gallon of gasoline ($) at all the various gas stations around town on a given day. Take a random sample of size 5 from this population.

2.59 3.01 3.15 2.83 2.79 2.59 2.96 3.05 3.19 3.03 2.65 2.74 2.83 2.69 3.05 3.10 2.89 2.84 2.63 3.11 2.76 2.89 2.90 3.09 3.05 2.71 2.84 2.90 2.75 2.90 2.56 2.89 2.76 2.87 2.92 3.05 3.09 2.57 3.20 2.76

a) Describe the individual, variable, population and sample.

b) A description of the process you went through to actually collect the random sample.

c) The work showing the calculation of the mean and standard deviation by hand. (You may use a basic calculator for the arithmetic.)

d) A sentence explaining the meaning of the standard deviation in terms of the gasoline prices.

Consider the following situation: Electrical engineers have a device that tests for battery life (in minutes) by placing a battery under a controlled electrical load and measuring how long it lasts. They are interested in comparing the performance of 4 brands of batteries. They replicated the experiment 4 times by randomly assigning a battery brand to be used in the electrical load device each time they measured battery life. In other words, they made 16 ‘runs’ and randomized the order in which the battery brands were used.

The data they obtained was:

1. State the Null and Alternative Hypothesis in words (both hypotheses) and using statistical notation (null hypothesis only).

2. Compute the means and sample standard errors for the brands. Upload the file. This can be an Excel spreadsheet, a photo/screenshot/scanned image.

3. Compute the sums of squares for Treatment, Error, and Total, and complete the ANOVA table below. For each SS, MS, and F calculation round to nearest whole number. For example, calculate SS > round to nearest whole number. Use that SS to calculate MS > round to nearest whole number. Use that MS to calculate F > round to nearest whole number.

4. Using the F - table and your ANOVA table results, what is the critical F-value for a test of the hypothesis at the 5% level of significance?

5. Based on your F-test statistic and F-critical value, write a complete conclusion of your hypothesis test.

6. What is the value from the Tukey table you will used to calculate the Tukey comparisons?  

7. Construct mean comparisons using the Tukey method and upload your results. Be sure to provide the Tukey W value (i.e. the value you calculated by which you compared the treatment means) and the letter grouping for each of the treatment means. Based on these Tukey comparisons, what battery brand(s) would you conclude differ in mean lifetime? This upload can be, for example, a photo taken of your work and an upload of that image.

8. Now use Minitab to conduct this analysis. Upload an image of your your Minitab output that shows your ANOVA table and grouping information of Tukey mean comparisons.

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 74 type K batteries and a sample of 46 type Q batteries. The mean voltage is measured as 8.65 for the type K batteries with a standard deviation of 0.832, and the mean voltage is 9.02 for type Q batteries with a standard deviation of 0.732. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1 be the true mean voltage for type K batteries and μ2 be the true mean voltage for type Q batteries. Use a 0.05 level of significance.

Compute the value of the test statistic. Round your answer to two decimal places.

Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places. (reject null if z is greater than or less than the decision rule)

Make the decision for the hypothesis test.

An advocacy group claims that Blacks/African-Americans are over-represented in the incarcerated population. In other words, they are claiming that there is a higher percentage of Blacks/African-Americans in the incarcerated population than in the general US population. A random sample of 150 US residents is sampled and 26 identify as Black/African-American. In another random sample of 40 US incarcerated individuals, 14 identify as Black/AfricanAmerican. Is there enough evidence to support the group’s claim at the 1% level of significance?

A. State the claim mathematically. Is the claim the null or alternative hypothesis?

B. State your hypotheses.

C. Determine the test of significance (t-test or z-test) and justify your choice.

D. State the standardized test statistic.

E. State the p-value.

F. State the correct decision of the test.

G. Interpret the decision in the context of the claim.

I really need help as soon as possible with this question, thank you!

In an annual report to investors, an investment firm claims that the share price of one of their bond funds had very little variability. The report shows the average price as $⁢20.00 with a variance of 0.18. One of the investors wants to investigate this claim. He takes a random sample of the share prices for 22 days throughout the last year and finds that the standard deviation of the share price is 0.2207 Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.01 Assume the population is normally distributed.

Step 2: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to THREE decimal places.

Step 3: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4: Make the decision.

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 133 with standard deviation of 20, and the mean length of two-year-old spotted flounder is 156 with a standard deviation of 24. The distribution of flounder lengths is approximately bell-shaped.

(a) Anna caught a one-year-old flounder that was 145 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places.

(b) Luis caught a two-year-old flounder that was 195 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places.

(c) Joe caught a one-year-old flounder whose length had a z-score of 1.3. How long was this fish? Round the answer to at least one decimal place.

(d) Terry caught a two-year-old flounder whose length had a z-score of −0.6. How long was this fish? Round the answer to at least one decimal place.

1) We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.

Hence, there are 80 cards in the deck with 16 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.

i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?
Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a flush that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?
Round your answer to 7 decimal places.

j) How many different ways are there to get a straight that is not a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a straight that is not a straight flush is  
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?
Round your answer to 7 decimal places.

2) Given the following information, answer questions a - d.
P(A)=0.48P(A)=0.48
P(B)=0.41P(B)=0.41
A and B are independent.
Round all answers to 5 decimal places as needed

a) Find P(A∩B).

b) Find P(A∪B).
c) Find P(A∣B).  

d) Find P(B∣A).  

Given the following information, answer questions e - g.
P(A)=0.48P(A)=0.48
P(B)=0.41P(B)=0.41
A and B are dependent.
P(A|B) = 0.14
Round all answers to 5 decimal places as needed

e) Find P(A∩B).     

f) Find P(A∪B)

g) Find P(B∣A).

SAVE OUTFILE = ‘\\Client\H$\Desktop\car.sav'.

explains what this part does in SPSS

A Gallup poll asked a random sample of 1000 adults nation-wide the following question:: "Are you in favor of the death penalty for a person convicted of murder?" 71% of the people in the sample answered "Yes".

1. A 95% Confidence Interval for the percent of all adults nation-wide in favor of the death penalty is (Hint: Fill in the first blank with the sample % and the second with the margin of error.)

（ ） % +/- （ ）%

A recent CBS New poll randomly sampled 1,142 adults nationwide asking them the following question:

"As you may know, the legal drinking age is 21. Would you approve or disapprove of states lowering the drinking age to 18, if the states felt that would give the police more time to enforce other laws?" 24% answered that they approved.

1. What is the expected value for the percent of all US adults who would say they approve of lowering the drinking age to 18, if the states felt that would give the police more time to enforce other laws? （ ）%

2. What is the SD of the sample? (Round to 3 decimal places.)

3. Calculate the SE of the percentage of people in the sample who answered "Approve". (Round to 2 decimal places.)

A poll is given, showing 75% are in favor of a new building project. If 138 people are chosen at random, answer the following. What is the probability that exactly 103 of them are in favor of a new building project? What is the probability that less than 103 of them are in favor of a new building project? What is the probability that more than 103 of them are in favor of a new building project? What is the probability that exactly 110 of them are in favor of a new building project? What is the probability that at least 110 of them are in favor of a new building project?

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 48% of all such batches contain no defective components, 29% contain one defective component, and 23% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.