Suppose three students are selected at random. Let A be the random 
variable representing the number of ABM students that are selected.

16. What is the probability that there will be no ABM student selected?
A. 8/27      B. 4/9      C. 19/27      D. 1

17. What is the probability that at most 2 ABM students are selected? (2 points)
A. 0      B. 0.2222      C. 0.4444      D. 0.9630

18. What is the probability that less than 2 ABM students are selected? (2 points)
A. 0.2222      B. 0.7407      C. 0.9630      D. 1

19. What is the mean of the probability distribution of the random variable A? (2 
points)
A. 0.5      B. 0.67      C. 1      D. 1.3

20. What is the variance of the probability distribution of the random variable A? (2 
points)
A. 0      B. 0.33      C. 0.44      D. 0.66

The probability distribution for the random variable x follows.
x------f(x)
20-----0.21
25-----0.11
32-----0.27
37-----0.41

1. f(x) is greater than 0 for all x. Is this a valid probability distribution?

2. What is the probability that x = 32?

3. What is the probability that x is less than or equal to 25?

4. What is the probability that x is greater than 32?

Apply the concept of the Central Limit Theorem to answer the 
following.
Numbers 1 -3: Twenty (20) ABM students were selected at random from the respondents. 
Assuming that the population standard deviation of the GWA of ABM students is 3.3912. 
1. What is the probability that their mean GWA is above 86? (2 points)
A. 0.0005

B. 0.0143

C. 0.9861

D. 0.9995

2. What is the probability form that describes the probability of number 1?
A. P(X>86)

B. P(X<86)

C. P(𝑋̅>86)

D. P(X<86)

3. Which normal distribution best describes the probability of number 1

A group of visitors consists of 15 students from the University of Oxford and 20 students from Leeds University. Among students from Oxford were 8 females and among the Leeds students were 5 females. A student was selected at random to give a vote of thanks at the of the visit. 

(a) What is the probability that the student is a female?

(b)Suppose that the female student is selected, what is the probability that the student comes from Leeds?

(c) Suppose that the student is selected is a female. What is the probability that the student comes from the University of Oxford?