Please Show Calculations:

1. The table below provides the grade categories along with the number of students obtaining a particular grade in the last five years in a difficult English course at a Caribbean University.

Based on the data, what is the probability that a currently enrolled randomly selected student will obtain an A?

a. 0

b. 0.16

c. 0.09

2. The random variable X denotes the number of times students at a certain university visit their Facebook page in a day. The table below gives the probability distribution of X

If a student from the university is randomly selected, what is the probability that he or she visits Facebook more than 3 times a day?

a. 0.361

b. 0.25

c. 0.639

3. The random variable X represents the number of 500ml bottles of water drank by a sample of men in a particular day while Y represents the same information for women. The probability distributions of X and Y are given below.

Based on the data, which of the following is true?

a. The average man drinks about 1,375ml of water a day

b. Men generally drink more water than women.

c. The average woman drinks about 105ml more water per day than the average man.

4. The table below provides the grade categories along with the number of students obtaining a particular grade in the last five years in a difficult English course at a Caribbean University.

Based on the data, what is the probability that a currently enrolled randomly selected student will obtain a C or a D?

a. 0.29

b. 0.37

c. 0.66

5. Which of the following is a discrete random quantitative variable

a. X = the number of books in the bag of your best friend

b. X = the number of phones owned by a randomly selected taxi driver

c. X = the amount of money in the wallet of a randomly selected USC student

A.For questions 1&2, determine whether each compound event described below is mutually inclusive, mutually exclusive, independent, or dependent. Explain your choice.

1. Rolling a 6 on a die and choosing a queen from a deck of cards. (See Ex. 2)

2. A teacher has a prize bag from which she will choose prizes for two students. The bag contains 8 tootsie rolls and 10 lollipops. She will choose for student 1, then for student 2. (See Ex. 3)

B. Suppose that Adam rolls a fair six-sided die and a fair eight-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the eight-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.

3. What is P(A), the probability that the six-sided die is an even number?

4. What is P(B), the probability that the eight-sided die is an odd number?

5. What is P( A and B), the probability that the six-sided die is an even number and the eight-sided die is an odd number?

6. Are events A and B independent? Why or why not?

The average annual number of jobs available for registered nurses is 103935 if we assume a normal distribution with a standard deviation of 8039 find the probability there will be between 102935 and 104085 nursing jobs available

In a group of 5 married couples, five different people are randomly selected. What is the probability of a couple being selected? Find the expected value of the number of couples selected among the five people.

For a large number of independent draws from a box, will standard deviation, range of draws and proportion of 1's in draws from a 0-1 box have a normally distributed probability histogram?

5 people from group are given an ID ranging from 1-9 independent from each other's ID. What is the probability that at least 2 people share an ID number?

draw six cards at random from a deck of 52 playing cards 60 times with replacement. Let X be the number of queen cards.

Find the probability distribution of X and Var (x)