Probability Theory

Q5. There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these.

a. What is the probability that the student gets exactly 7 correct?

b. What is the probability that the student gets exactly 8 correct?

c. What is the probability that the student gets exactly 9 correct?

d. What is the probability that the student gets exactly 10 correct?

e. What is the probability that the student gets more than 6 correct?

f. What is the probability that the student gets 0 correct?

Q6. Ma Huateng is the top salesman for his company. Records indicate that he makes a sale on 70% of his sales calls. If he calls on four potential clients, what is the probability that he makes exactly 3 sales? What is the probability that he makes exactly 4 sales?

Q7. If 10% of all SSD produced are defective, what is the probability that there will be exactly 1 defect in a random sample of 5 of these? What is the probability that there will be no defects in a random sample of 5?

Q8. The mean starting salary for DBA graduates is USD 6,280.00. Assume that the distribution for starting salaries follows a normal distribution with a standard deviation of USD 300.00. What percent of the graduates have starting salaries?

a. Between USD 5,000.00 and USD 10,000.00?

b. More than PHP 10,000.00?

Q9. A study of long-distance phone calls made from the corporate office of the Pepsi Bottling Group, Inc. showed the calls follow a normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes.

a. What fraction of the calls last between 4.2 and 5 minutes?

b. What fraction of the calls last more than 5 minutes?

c. What fraction of the calls last between 5 and 6 minutes?

d. What fraction of the calls last between 4 and 6 minutes?