4 questions work on excel

1. The following table shows responses from students who were asked about their undergraduate major and intent to pursue an MBA degree as a full time or part time student.

a) Develop a joint probability table for this data (6 pts)

b) What are the marginal probabilities for each undergraduate major and each enrollment status (2 pts)

c) Comment on which undergraduate major produces the most potential MBA students.(2 pts)

d) If a student plans to attend classes fulltime what is the probability that the student was an undergraduate Science major (2 pts)

e) If the student was an undergraduate business major, what is the probability that the student intends to attend school part time (2 pts)

f) Let P denote the event that the student intends to be enrolled part time and S denote the event that the student was an undergraduate science major. Are the events P and S independent? Justify your answer (4 pts).

2. The probability for a random variable x is as follows:

a. Is this probability distribution valid? Explain (4 pts)

b. What is the probability that x=32? (2 pts)

c. What is the probability that x is less than or equal to 35 (2 pts)

d. What is the probability that x is greater than or equal 30 (2 pts)

3. The following responses are from 1050 adults aged 18 and over who were asked “How many cups of coffee if any do you drink on an average day?”

a. Develop a probability distribution for x (2 pts)

b. Compute the expected value of x (4 pts)

c. Compute the variance of x (6 pts)

4. Consider a binomial experiment with n =10 and p =.15

a. Compute the probability of 1 success, f(1) (3pts)

b. Compute the probability of 0 successes, f(0) (3 pts)

c. Compute P(x ≥ 2) (2 pts)

d. Compute E(x) (2 pts)

Note for a binomial distribution, E(x) = n*p