Lab Discrete Distributions

Transcription

1 4.2.1 Lab 8 Lab Discrete Distributions Name: Learning Objectives: Find probabilities with a table. Find binomial probabilities. Find the Mean, Variance and Standard Deviation of a Binomial Distribution. Expected value problems. Defective Parts Baiers Electronics manufactures computer parts that are supplied to many computer companies. Despite the fact that two quality control inspectors at Baiers Electronics check every part for defects before it is shipped to another company, a few defective parts do pass through these inspections undetected. Let x denote the number of defective computer parts in a shipment of 400. The following table gives the probability distribution of x. x p(x) How many defective computer parts would you expect to receive in a shipment of 400? 1. Find each probability below. 2. What is the probability that a shipment of 400 computer parts has no defective parts? 3. What is the probability that at least one computer part in a shipment of 400 is defective? What is the probability that less than four computer parts in a shipment of 400 are defective? Page 101

2 Hospital ER A review of emergency room records at a rural hospital was performed to determine the probability distribution of the number of patients entering the emergency room during a 1-hour period. The following table lists the distribution.: Patients per hour, x Probability, p(x) How many patients are expected to enter the emergency room during a 1-hour period? What is the standard deviation of the number of patients entering the emergency room during a 1-hour period? 6. Find the following probabilities. 7. What is the probability that the number of patients entering the emergency room during a 1-hour period is at least two? What is the probability that the number of patients entering the emergency room during a 1-hour period is not more than eight? What is the probability that the number of patients entering the emergency room during a 1-hour period exceeds eight? 9. Page 102

3 Hospital ER A review of emergency room records at a rural hospital was performed to determine the probability distribution of the number of patients entering the emergency room during a 1-hour period. The following table lists the distribution.: Patients per hour, x Probability, p(x) Find the following probabilities. 10. What is the probability that the number of patients entering the emergency room during a 1-hour period is less than nine? Would it be unusual to have more than eight patients enter the emergency room during a 1-hour period? (Hint: use the 5% rule introduced in Section 3.1) P (x >7) P (x <3) P (5) Graph the probability distribution in the space below. Page 103

4 16. Binomial Tables Let X be a binomial random variable with n =5andp =0.30. Use the Binomial Tables (Link Below) to obtain the correct probability distribution needed to answer probability questions. (a) Write your distribution table in the space below. Find each probability. P (X =5) P (X 1) 17. College Degrees Nearly 40 percent of working-aged Americans now hold a college degree, according to a new report from the Lumina Foundation. Suppose a group of 32 Americans are randomly selected and asked if they hold a college degree or not. Let x denote the number of Americans in this sample of 32 who say that they hold a college degree. Obtain the binomial probability distribution table necessary to answer the questions given below. You do NOT have to write your probability distribution table on this paper. (a) How many college graduates would you expect to be in the group of 32? What is the standard deviation of the number of college graduates in the group of 32? (a) What is the probability there are 2 college graduates in the group of 32? (d) What is the probability there are 3 or fewer college graduates in the group? (d) (e) What is the probability that there are at least 6 college graduates are in the group? (e) Page 104

5 18. Marketing A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that 70% of all people like this hamburger. On a certain day, eight customers bought it for the first time. (a) Let x denote the number of customers in this sample of eight who will like this hamburger. Using the binomial probabilities table or your calculator, obtain and write down in the space below the probability distribution of x, and draw a graph of the probability distribution. Determine the mean and standard deviation of x. How many of the eight people who bought the burger would you expect to like the burger? (d) Using the probability distribution of part a, find the probability that exactly three of the eight customers will like this hamburger. 19. Basketball Michael Jordon is a retired American professional basketball player. Jordan played 15 seasons in the National Basketball Association for the Chicago Bulls and Washington Wizards. Jordon s career stats indicate that he makes 83.5% of the free throws he tries. Assuming this percentage will hold true for future attempts, find the probability that in the next ten tries, the number of free throws he will make is (a) exactly 9 exactly 7 (a) Page 105