A corporation is trying to decide whether to open a new factory outlet store. The store will have high, medium, or low demand. Before it decides whether to open the store, the corporation can pay $7,000 immediately for a market survey. The market survey can predict 'high,' 'medium,' or 'low' demand. If the actual demand of the store will be high, there is a 0.6 probability the survey will predict 'high' demand, a 0.06 probability the survey will predict 'medium' demand, and a 0.34 probability the survey will predict 'low' demand. If the store will actually have medium demand, there is a 0.26 probability the survey will predict 'high' demand, a 0.36 probability the survey will predict 'medium' demand, and a 0.38 probability the store will predict 'low' demand. If the store will actually have low demand, there is a 0.04 probability the survey will predict 'high' demand, a 0.14 probability the survey will predict 'medium' demand, and a 0.82 probability the survey will predict 'low' demand. If the corporation decides not to take the market survey, there is a 0.22 probability the store will have high demand, a 0.57 probability the store will have medium demand, and a 0.21 probability the store will have low demand. If the corporation decides to open a store, the immediate cost of opening the store is $382,000, and the store must remain open for exactly 4 years. If demand is high, the store will EARN $0.5 million for each year that the store is open. If demand is medium, the store will EARN $200,000 for each year that the store is open. If demand is low, the store will LOSE $113,000 for each year that the store is open. You should assume that demand remains the same for each year that the store is open. There is no salvage value, and you can ignore taxes. If the corporation decides not to open a store, the corporation has a net present worth = $0 minus the cost of the survey (if the corporation takes the survey). The corporation's MARR is 12%. The corporation will choose the alternative with the largest expected net present worth (NPW). What is the expected NPW of the best alternative?

In San Francisco, 30% of workers take public transportation daily. In a sample of 10 workers,

a.Clearly state what the random variable in this problem is?

b.What is an appropriate distribution to be used for this problem and why?

c.What is the probability that exactly three workers take public transportation daily?

d.What is the probability that NONE of the workers take public transportation daily?

e.What is the probability that more than five workers take public transportation daily?

f.What is the probability that less than seven workers take public transportation daily?

g.What is the probability at least two but no more than eight workers take public transportation daily?

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of

2.0

liters

and a standard deviation of

0.05

liter. Suppose you select a random sample of

25

bottles.

a. What is the probability that the sample mean will be between

1.99

and

2.0

liters​?

b. What is the probability that the sample mean will be below

1.98

liters?

c. What is the probability that the sample mean will be greater than

2.01

​liters?

d. The probability is

90%

that the sample mean amount of soft drink will be at least how​ much?

e. The probability is

90​%

that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​mean)?

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of

2.0 liters and a standard deviation of 0.05 liter. Suppose you select a random sample of 25 bottles.

a. What is the probability that the sample mean will be between 1.99 and 2.0 liters​?

b. What is the probability that the sample mean will be below 1.98 liters​?

c. What is the probability that the sample mean will be greater than 2.01 ​liters?

d. The probability is 99​% that the sample mean amount of soft drink will be at least how​ much?

e. The probability is 99​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?

There are A, B, and C types of problem set, and each type of problem set contains 3000, 2000, 5000 problems, respectively. Suppose you can solve A-type problem with 90% probability, B-type problem with 20% probability, and C-type problem with 60% probability. To pass graduation exam, you must solve both of two questions randomly chosen from the total problem set (out of 10,000 problems). Answer the following questions:

1) What is the probability that you pass the graduation exam? 2)

What is the probability that you have solved one or more A-type questions when you passed the exam?

In a group of 150 students, 60 like "vegetables", 40 like "fruits" and 30 like both. A student is selected at random,
a) What is the probability that he/she likes "vegetables" or "fruits"?
b) What is the probability that he/she does not like "fruits"?
c) What is the probability that neither fruits nor vegetables?
d) What is the probability that he/she likes fruits, but not vegetables?
e) What is the probability that he/she likes "fruits" since he/she likes "vegetables"?
The answers are:

a:0.4667

b:0.7333

c:0.5333

d:0.0667

e:0.50

I need to know how to get to those answers

A? government's department of transportation reported that in? 2009, airline A led all domestic airlines in? on-time arrivals for domestic?flights, with a rate of 83.9%Complete parts a through e below.

a. What is the probability that in the next six? flights, exactly four flights will be on? time?The probability is

.Round to four decimal places as? needed.)

b. What is the probability that in the next six? flights, two or fewer will be on? time?

c.What is the probability that in the next six? flights, at least four flights will be on? time?The probability is

?(Round to four decimal places as? needed.)

d. What are the mean and standard deviation for this? distribution?

e. Construct a histogram for this distribution. Choose the correct graph below.

About 43% of students are dog owners. 20 students are selected at random. Indicate what key was used on your calculator. Round your answers to three significant digits.

a. What type of a distribution is the above?

b. What I s the probability that exactly 6 students are dog owners?

c. What is the probability that less than 4 students are dog owners?

d. What is the probability that more than 4 students are dog owners?

e. What is the probability that at most 15 students are dog owners ?

f. What is the probability that between 9 and 15 students (inclusive) are dog owners? (2 points)

A car wash offers both a regular wash and a deluxe wash for their customers. They track their customers over time and determine that a customer orders the deluxe wash with a probability of 0.3. They also offer air fresheners for their customer for a nominal fee and find that regular wash customers get an air freshener with a probability of 0.45, and deluxe wash customers get an air freshener with probability 0.8. Assume that the car wash only offers the regular and deluxe packages.

a.) What is the probability that a customer gets an air freshener, regardless of the type of wash they ordered?

b.) What is the probability a customer ordered the deluxe package, provided that you know they purchased an air freshener?

**Please work in R**

In a group of students, there are 2 out of 18 that are left-handed.

a. Assuming a low-informative prior probability distribution, find the posterior distribution of left-handed students in the population. Summarize your results with an estimation of the mean, median, mode, and a 95% credible interval. Plot your posterior probability distribution.

b. According to the literature, 5 to 20% of people are left-handed. Take this information into account in your prior probability and calculate a new posterior probability distribution. Summarize your results with an estimation of the mean, median, mode, and a 95% credible interval. Plot your posterior probability distribution.