Ten (10) HUMSS students were selected from the respondents. Assuming 
that the population standard deviation of the GWA of HUMSS students is 3.6752. 
4. What is the probability that their average grade is below 88? (2 points)
      A. 0.3483         B. 0.409           C. 0.6064         D. 0.6517
5. What is the probability form that describes the probability of number 4?
      A. P(X<88)       B. P(X>88)       C. P(𝑋̅<88)       D. P(𝑋̅>88)

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

Fifty (50) STEM students were selected at random from the respondents.
7. What is the probability that their average grade is between 86 and 88? (2 points)
      A. 0.0001       B. 0.2235       C. 0.3014       D. 0.9999
8. What is the probability form that describes the probability of number 7?
      A. P(86<𝑋̅<88)       C. P(86<X<88)
      B. P(86>𝑋̅>88)       D. P(86>X>88)

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?