Exercise #1

Mention an advantage and disadvantage that you consider when using the binomial probability distribution. (2 points)

Exercise #2

The probability distribution of a random variable x is presented below. x f (x)

20 0.35

25 0.10

30 0.15

35 0.40

Answer me:

Is this distribution valid, that is, is it considered a probability distribution? Explains. (2 points)

What is the probability that x = 30? (1 point)

What is the probability that x is less than or equal to 25? (1 point)

What is the probability that x is greater than 30? (1 point)

Exercise #3

Below is a probability distribution.

x Probability f(x) 0 0.10

1 0.14

2 ?

3 0.22

4 0.15

5 0.08

Calculate and answer:

Find P(4). (2 points)

What is the expected (average) value of the number of services? (3 points)

What is the variance of the number of services? (3 points)

What is the standard deviation? (2 points)

Exercise #4

The probability distribution of the ratings established by employees on the relationship they have with their supervisors range from 1 (poor) to 5 (excellent).

Qualification of the employee's relationship with supervisor (x) Supervisor A f (x) Supervisor B f (x)

1 0.07 0.14

2 0.09 0.10

3 0.03 0.12

4 0.40 0.36

5 0.41 0.28

What is the expected (average) value of the securities offered to supervisor A's rating? (3 points)

What is the expected (average) value of the securities offered to supervisor B's rating? (3 points)

Calculates the variance of the values offered to the rating of supervisor A. (3 points)

Calculate the standard deviation of the values offered to supervisor B's rating? (3 points)

Compare the satisfaction with supervisor A with that with supervisor B. (2 points)

Exercise #5

Use the binomial distribution table to find the binomial probabilities for these cases:

n = 10, p = .1, k = 3 (2 points)

n = 14, p = .6, k = 7 (2 points)

n = 25, p = .5, k = 14 (2 points)

Exercise #6

Consider a binomial experiment with n = 22 and p = 0.70. Use the binomial formula to calculate:

P(x = 15) (3 points)

average (2 points)

variance (2 points)

standard deviation (2 points)

Exercise #7

40% of NUC University students use their own car to get to college. What is the probability that in a sample of 15 students, six (6) students will use their own car? (Use the binomial formula to solve the exercise.) (3 points)

Exercise #8 40% of Americans who travel by car look for gas stations and food stores that are nearby or visible from the road. Suppose a random sample of n = 30 Americans traveling by car are asked how they determine where to stop to buy food and pour gas. Let x be the number of the responding sample looking for gas stations and food stores that are nearby or visible from the road (Mendenhall et al., 2015). (Use the binomial formula to solve the exercise.) Answer me:

What is the mean if x=12? (2 points)

What is the variance of x? (2 points)

Calculate the interval 2 (2 points)

Which values of the binomial random variable x fall in this range? (2 points)