High blood pressure: A national survey reported that

34%

of adults in a certain country have hypertension (high blood pressure). A sample of

24

adults is studied. Round the answer to at least four decimal places.

Part 1 of 4

(a) What is the probability that exactly

5

of them have hypertension?

Part 2 of 4

(b) What is the probability that more than

7

have hypertension?

Part 3 of 4

(c) What is the probability that fewer than

3

have hypertension?

Part 4 of 4

(d) Would it be unusual if more than

9

of them have hypertension?

The physicians in previous problem have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim their experience enables them to use Bayes’ theorem to make the following statements of probability:

probability of a favorable market given a favorable study -----0.82 probability of an unfavorable market given a favorable study 0.18 probability of a favorable market given an unfavorable study 0.11 probability of an unfavorable market given an unfavorable

study-- 0.89 probability of a favorable research study ----------0.55 probability of an unfavorable research study----------------------0.45

a) Develop a new decision tree for the medical professionals to reflect the options now open with the market study.

b) Use the EMV approach to recommend a strategy.
c) What is the expected value of sample information? How much might the

physicians be willing to pay for a market study?
d) Calculate the efficiency of this sample information.

DATA: Grades

A- 10     B- 2     C- 1 D- 0   F- 2

Q23. a) If a committee with 2 student members is to be formed, what is the probability of forming a committee with one A grade and one F grade student?

Q24. If a committee with 3 student members is to be formed, what is the probability of forming a committee with two A grade and one B grade student?

Q25.If the records show that, the probability of failing (with grade F) this course is p, what is the probability that at most 2 students out of 15 fail this course? {Hint: use binomial distribution}

Q26.If the records show that, the probability for a student to get a grade B this course is p, what is the probability that exactly 4 students out of 15 will have a grade B for the course? {Hint: use binomial distribution}

Q27.What is the probability of selecting a grade A student for the first time either in 2nd or 3rd selection?

You’re waiting for Caltrain. Suppose that the waiting times are approximately Normal with a mean of 12 minutes and a standard deviation of 3 minutes. Use the Empirical Rule to estimate each of the following probabilities without using the normalcdf function of your calculator:

a) What is the probability that you’ll wait between 9 and 15 minutes for the train?

b) What is the probability that you’ll wait between 6 and 18 minutes for the train?

c) What is the probability that you’ll wait between 3 and 21 minutes for the train?

d) What is the probability that you’ll wait more than 12 minutes for the train?

e) What is the probability that you’ll wait between 12 and 18 minutes for the train?

f) What is the probability that you’ll wait between 3 and 18 minutes for the train?

g) What is the probability that you’ll wait more than 21 minutes for the train?

Suppose you are looking at the population of 8,000 students that are freshman at UTEP. You want to determine on average how many hours a week they work each week. Let’s call that number ?. You decide to take a sample of 100 of them.

• 1) How many data points are there in this space?
• 2) How many ways can you choose your subest of 100 students? Is it greater or less than the answer above.
• 3) How do you calculate the “point estimate” of one of those subsets of 100 students?
• 4) How many actual subsets of 100 students do you have as a researcher?
• 5) What does the Central Limit Theorem say about all the possible point estimates that can occur from the possible 100-student subsets? Draw a graph.
• 6) What value is the center of that curve? Please label it on the graph above.

Let’s just say the standard deviation of those 8,000 students is 5.

• 1) What is the formula for standard deviation of a population the 8,000 students (please make sure the summation sign has a starting and ending number)? Can it ever be negative? In our example, what are the units of the standard deviation?
• 2) What does the Central Limit Theorem say about the standard deviation of the curve discussed in question 5) above?
• 3) What is the standard deviation in our example?
• 4) What is the probability that a randomly picked sample has a point estimate within .5 of
  the actual mean ??
• 5) What is the probability that a randomly picked sample has a point estimate within 1 of
  the actual mean ??
• 6) Do you know whether our point estimate is higher or lower than the mean?

A certain electric power company maintains that its average rate of critical home electrical power failures is 1.3 failures per day. From analyzes carried out in previous years, it is known that critical failures appear according to a Poisson process. The failure repair team in electrical networks of that company maintains that the failure rate received per day is higher and chooses to make a count of the number of failures reported to it during the month of May to prove it.
to.

a.If we assume that what the electric power company says is true:
i.What is the expected number of failures during the month of May?
ii. What is the probability that 41 failures or fewer will occur during that month?
b. Indicate what the hypothesis is and its denial.
c. Tell what the probability distribution of the statistic is if the hypothesis is assumed to be true.
d. If the team establishes the criterion that they will reject the hypothesis if the variable of interest (statistical) exceeds the mean by 1.8 standard deviations, it establishes:
i. What is the rejection criterion according to the value that the variable (statistic) takes in the month of May?
ii. What is the level of significance (type 1 error) with which the repair team would reject the hypothesis?

e.At the end of May, the count of failures reported to the repair team was made in the month and they found that there were 49.
i. How many standard deviations from the mean is the result obtained in the sample?
ii. What is the p-value of the result found?
f. Is the hypothesis rejected or accepted? Be specific in explaining why it is rejected or not rejected. Indicates the level of significance with which the hypothesis is rejected or not.
g. It concludes in the context of the problem.
[Answer: 40.3, 0.5848, X≥52, 0.0431, 1.37, 0.1008]

Cholesterol is a type of fat found in the blood. It is measured as a concentration: the number of milligrams of cholesterol found per deciliter of blood (mg/dL). A high level of total cholesterol in the bloodstream increases risk for heart disease. For this problem, assume cholesterol in men and women follows a normal distribution, and that “adult man” and “adult woman” refers to a man/woman in the U.S. over age 20. For adult men, total cholesterol has a mean of 188 mg/dL and a standard deviation of 43 mg/dL. For adult women, total cholesterol has a mean of 193 mg/dL and a standard deviation of 42 mg/dL. The CDC defines “high cholesterol” as having total cholesterol of 240 mg/dL or higher, “borderline high” as having a total cholesterol of more than 200 but less than 240, and “healthy” as having total cholesterol of 200 or less. A study published in 2017 indicated that about 11.3% of adult men and 13.2% of adult women have high cholesterol.

1) A researcher measures the total cholesterol of a randomly selected group of 36 adult women, and counts the number of them who have high cholesterol. (Assume that 13.2% of adult women have high cholesterol.)

a. What is the probability that exactly 4 of these 36 women have high cholesterol?

b. What is the probability that 8 or less of these 36 women have high cholesterol?

2) A doctor recommends drastic lifestyle changes for all adults who are in the top 5% of total cholesterol levels.

a. What total cholesterol level is the cutoff for the top 5% of women? (Round to 1 decimal place.)

b. What total cholesterol level is the cutoff for the top 5% of men? (Round to 1 decimal place.)

1. A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a par- ticular time, and let Y denote the number of hoses on the full service island in use that time. The joint pmf of X and Y appears in the accompanying tabulation.

a. WhatisP(X=1andY =1)?

b. ComputeP(X≤1andY ≤1).

c. Compute P(X ̸= 1 and Y ̸= 1).

d. Compute the marginal pmf of X and Y. Using pX(x), what is P(X ≤ 1)?

e. Are X and Y are independent? Explain.

2. Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable – X for the right tire and Y for the left tire, with joint pdf

?K(x2 +y2), 20≤x≤30, 20≤y≤30,

f(x,y) =

0, otherwise

a. What is the value of K?

b. What is the probability that both tires are underfilled?

c. What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Hint: Draw the shaded region first and then find the boundary of the integration.)

d. Determine the marginal pdf of X and Y . e. Are X and Y independent? Explain.
f. Find E(X) and E(Y ).

question 1

The following table provides a description for the project Z.

1. What is the critical path of this project?

2. What is the duration of this project? (before crashing)

3. If your task is to crash this project by 2 days, what is the most efficient cost of doing it? (Just input the number with no decimals or dollar signs

question 2

The expected duration of the project (average) is 30 days and variance is 16.

1. What is the probability that the project will be completed on day 32 or earlier?

2. Suppose the official deadline for the project is 34 days. What is the probability that the project will be delayed?

question 3

A restaurant has tracked the number of meals served at lunch over the last four weeks. The data show little in terms of trends, but do display substantial variation by day of the week. Use the following information to determine the seasonal (daily) indices for this restaurant.

a.

B.

c.