On Tuesday, Sara’s Produce is expecting to receive Package A containing $2,000 worth of food. Based on past experience with the delivery service, the owner estimates that this package has a chance of 10% being lost in shipment.

On Wednesday, Sara’s Produce expects Package B to be delivered. Package B contains $1,000 worth of food. This package has a 4% chance of being lost in shipment.

1. Construct [in table form] the probability distribution for the total dollar amount of losses for package A and B. [4 points]

In the table, make sure you specify:

- The possible outcomes for Sara’s total dollar amount of losses for packages A and B. Please note that this asks about the total dollar amount of losses, not the number of losses.

- For each dollar amount of losses, describe under what circumstances it would occur. In other words, what event(s) must happen for each dollar amount of losses to occur?

- For each of the possible outcomes, you identify in part [a], derive the probability of the outcome occurring.

2. Calculate the expected value of the total dollar amount of losses. [1 point]
3. The owner has calculated the variance for the total dollar amount of losses to be 398,400. Since you want to be sure you are using correct numbers in your evaluation, prove that the owner calculated the correct variance for the total dollar amount of losses. Show all work! [2 points]

QUESTION 3 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 25 years with a standard deviation of 5.1 years. A random sample of 36 students is selected. Compute the expected value of the sample mean. 5 points

QUESTION 4 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 25.5 years. A random sample of 55 students is selected. Compute the standard deviation of the sample mean. 5 points

QUESTION 5 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 3.81 years. What is the smallest sample size such that the standard deviation of the sample mean is 0.5 years or less? (Enter an integer number.) 10 points

QUESTION 6 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 3 years. A random sample of 36 students is selected. What is the probability that the sample mean will be less than 24.88 years? 10 points

QUESTION 7 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 3 years. A random sample of 36 students is selected. What is the probability that the sample mean will be greater than 23.22 years?

Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 71 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.32?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =0.3555 was wrong

B.Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 138 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.35?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer = 0.7736 was the wrong answer (Enter your answer as a number accurate to 4 decimal places.)

C.You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required?

n =
Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Let S be a set and P be a property of the elements of the set, such that each element either has property P or not. For example, maybe S is the set of your classmates, and P is "likes Japanese food." Then if s ∈ S is a classmate, he/she either likes Japanese food (so s has property P) or does not (so s does not have property P). Suppose Pr(s has property P) = p for a uniformly chosen s ∈ S. Suppose Ofer the Oracle has magic powers that allow him to check property P for any s, but it doesn’t always work since each time he relies on some (independently) generated random numbers to help him. If he says “Yes,” then s has the property. If s has the property, then he says “Yes” with probability at least q.

Suppose we let Ofer check property P on an element s a total of N times, and he responded “No” each time. Find a lower bound (i.e. a smaller number, but a useful one) for Pr(s does not have property P). Suppose p = 99/100 and q = 1/2, how many times should you let Ofer check probability P before you are 99% confident that s does not have property P?

1. Andrew plans to retire in 38 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 38 years will exceed 12%?

2. Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 120 mg/dl and σ = 10 mg/dl.

(b) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

Coleman Rich Control​ Devices, Inc., produces​ custom-built relay devices for auto makers. The most recent project undertaken by Rich requires 14 different activities.​ Rich's managers would like to determine the total project completion time​ (in days) and those activities that lie along the critical path. The appropriate data are shown in the following table:          

​a) The expected completion time of the project​ = _______days ​(round your response to two decimal​ places).

The activities that represent the project's critical path are _____________________________

b) If the time to complete the activities on the critical path is normally distributed, then the probability that the critical path will be finished in 53 days or less = _______

c) Number of days that would result in 99% probability of completion = ______ days.

Make a program to simulate the end of the world as we know, containing the following features: NEEDED IN C++.

The world population according to all sci-fi movies will perish up to a certain percentage, given global: (a) earthquakes 10%, (b) tsunamis 20%, (c) volcanoes 10%, (d) freezing temperature from sudden ice age 10%, (e) crashing meteorites 10%, (f) widely spread fires 10%, (g) hunger 10%, (h) zombies 10%, and (i) hurricanes 10%;1) Implement a classnamed World; Class Worldinherited the Class CRandom;

2) In the Class Worldcreate methods named EarthQuakes; Tsunamis; Volcanoes; IceAge; Meteorites; Fires; Hunger; Zombies; and Hurricanes; Those methods are used to return/inform the death toll (in numbers and percentage) caused according to the respective event uniform probability: e.g. tsunamis rangeLow is 0 and rangeHigh is 20%;

3) The methods created in the previous step (item 2), should use the inherited Class CRandomto obtain the expected random probability;

4) In the Class World create a method named TotalSurvivorsthat informs in percentage what is the final earth's population that survived the Apocalypse/armageddon, compared with its current population currently estimated as 7 Billion;

5) In the Class World create a method named NewWorldthat will print the message: “Happy Ending! Total number of Survivors is: .... ”, if there is no survivors, then print the message: “No Happy Ending! There are no survivors.”

Problem 31. Calculate the expected value and variance of X for each of the following scenarios.

1. X = {0, 1} where each has equal probability. (A coin flip)

2. X = {1, 2, 3, 4, 5, 6} where each has equal probability. (A die roll)

3. X = {0, 1} with f(0) = 1/3 and f(1) = 2/3.

4. X = B(3, 0.35). (Use info from Problem 26.)(Problem 26. Let X = B(3, 0.35). Calculate each f(k) and the sum X 3 k=0 f(k).)

Problem 32. Calculate the expected value and variance of X = B(3, 0.35) by using Theorem 41. Compare the results to part 4 of Problem 31.

Problem 33. Let (X, f) be a CPD. Show that P(X = x) = 0 for any x ∈ X.

Problem 34. Consider f : R → R defined by f(x) = 1 1 + x 2 . Explain why f is not a PDF, and find a constant c so that cf is a PDF.

Problem 35. Let F be a CDF for a CPD (X, f). Find lim x→−∞ F(x) and limx→∞ F(x).