I. Discrete probability distribution. Answer the following:

1. The probability distribution for the random variable X is as follows

X f(x)

20 .20

25 .15

30 .25

35 .40

Whole 1.00

a. What is the probability that X=30?

b. What is the probability that X is less than or equal to 25?

c. Draw the graph of the aforementioned probability distribution.

d. What is the mean or expected value and variance of the probability distribution above?

II. choose the best answer

1. In a discrete probability distribution the sum of all the relative frequencies or probabilities must be:

a. Same as sample size

b. Equal to half of the average

c. equal to zero

d. equal to one

2. When drawing a graph of a discrete distribution, we must connect the points with a line. This statement is:

a. wrong

b. correct

3. The value of the random variable of the hypergeometric distribution,

a. Goes from minus infinity to plus infinity

b. goes from zero to one

c. goes from zero to infinity

d. Goes from zero to sample size

III. Hypergeometric Distribution

1. It is known that there are 200 computers made up of 120 Dells and 80 Gateways. If 10 computers were sent for repair. (Hypergeometric)

a. What is the probability that they will receive 3 Dell-branded ones?

b. What is the probability that they will receive Gateway-branded 7s?

c. In the long run, how many Dell computers will be repaired?

2. It is known that in a classroom there are 50 students, 36 are from Santurce and 14 from Bayamn. If 8 students are randomly interviewed. (Hypergeometric)

a. What is the probability that 3 students from Bayamn are interviewed?

b. What is the probability that 5 students from Santurce are interviewed?

c. In the long term, how many Santurce students will be interviewed?