Instructions:

In this task, you will work with one of the discrete probability distributions. You will calculate the binomial probability distribution, its mean, variance, and standard deviation. You must read the material presented in sections 5.1, 5.2, 5.3 and 5.5 of the textbook to complete the exercises assigned for this activity, with which your learning will be assessed. You must present the processes necessary to support the answer of the exercises and round the final resultsnot the intermediate values that appear during the calculationsto two decimal places, when necessary.

Exercise 1

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

Exercise 2

Next, the probability distribution of a random variable x is presented.

x f (x) 20 0.35 25 0.10 30 0.15 35 0.40 Answers: Is this distribution valid, that is, is it considered a probability distribution? Explain. (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 two ? 3 0.22 4 0.15 5 0.08 Calculate and answer: Find P(4). (2 points) What is the expected value (mean) 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 about the relationship they have with their supervisors ranges from 1 (poor) to 5 (excellent).

Qualification of the employee's relationship with the 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 value (mean) of the securities offered to the rating of supervisor A? (3 points) What is the expected (mean) value of the securities offered to rate supervisor B? (3 points) Calculate the variance of the values offered to the rating of supervisor A. (3 points) Calculate the standard deviation of the securities offered to qualify supervisor B? (3 points) Compare their satisfaction with supervisor A with that they have with supervisor B. (2 points) Exercise #5

1) 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

3) 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 the university. 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 grocery stores that are close to or visible from the road. Suppose a random sample of n = 30 Americans who travel by car are asked how they determine where to stop for groceries and gas. Let x be the number of the sample that responds that they look for gas stations and food stores that are close to or visible from the road (Mendenhall et al., 2015). (Use the binomial formula to solve the exercise). Answers:

What is the mean if x=12? (2 points) What is the variance of x? (2 points) Calculate the interval 2 (2 points) What values of the binomial random variable x fall in this interval? (2 points)