Free Powerpoint Templates ROHANA BINTI ABDUL HAMID INSTITUT E FOR ENGINEERING MATHEMATICS (IMK) UNIVERSITI MALAYSIA PERLIS ROHANA BINTI ABDUL HAMID INSTITUT E FOR ENGINEERING MATHEMATICS (IMK) UNIVERSITI MALAYSIA PERLIS

PROBABILITY DISTRIBUTION CHAPTER 3 PROBABILITY DISTRIBUTION (PART 3)

INTRO CONTINUE……

Example 3.3

SOLUTIONS Using table

In January 2003, the American worker spent an average of 77 hours logged on to the internet while at work. Assume that the population mean is 77 hours, the times are normally distributed, and the standard deviation is 20 hours. A person is classified as heavy user if he or she is in the upper 20% of usage. How many hours did a worker have to be logged on to be considered a heavy user? Example 3.4

SOLUTIONS Let X be the r.v. “hours of worker spent on internet” where X~N(77, 20 2 ).

3.4 NORMAL DISTRIBUTION NORMAL APPROXIMATION OF THE POISSON DISTRIBUTION NORMAL APPROXIMATION OF THE BINOMIAL DISTRIBUTION INTRODUCTION

3.4.2 Normal Approximation of the Binomial Distribution  When the number of observations or trials n in a binomial experiment is relatively large, the normal probability distribution can be used to approximate binomial probabilities. A convenient rule is that such approximation is acceptable when

Definiton 3.5

Continuous Correction Factor  The continuous correction factor needs to be made when a continuous curve is being used to approximate discrete probability distributions.

Example 3.5 In a certain country, 45% of registered voters are male. If 300 registered voters from that country are selected at random, find the probability that at least 155 are males.

Solutions Let X be the r.v. “number of male voters” where X~B(300, 0.45).

3.4 NORMAL DISTRIBUTION NORMAL APPROXIMATION OF THE POISSON DISTRIBUTION NORMAL APPROXIMATION OF THE BINOMIAL DISTRIBUTION INTRODUCTION

3.4.3 Normal Approximation of the Poisson Distribution  When the mean of a Poisson distribution is relatively large, the normal probability distribution can be used to approximate Poisson probabilities.  A convenient rule is that such approximation is acceptable when  Definition 3.6

Example 3.6 A grocery store has an ATM machine inside. An average of 5 customers per hour comes to use the machine. What is the probability that more than 30 customers come to use the machine between 8.00 am and 5.00 pm?

Solutions Let X be the r.v. “number of customers per hour” where X~P 0 (5). Let X be the r.v. “number of customers for 9 hours” where X~P 0 (45).

EXERCISE 1 According to a survey by Duit magazine, 27% of women expect to support their parents financially. Assume that this percentage holds true for the current population of all women. Suppose that a random sample of 300 women is taken. Find the probability that exactly 79 of the women in this sample expect to support their parents financially.

EXERCISE 2 Aonang Beach Resort Hotel has 120 rooms. In the spring months, hotel room accupancy is approximately 75%. I. What is the probability that 100 or more rooms are occupied on a given day. II. What is the probability that 80 or fewer rooms are occupied on a given day?

EXERCISE 3 In a university, the average of the students that come to the student health center is 5 students per hour. What is the probability that at least 40 students will come to the student health center from 9.00 am to 6.00 pm?

EXERCISE 4 Suppose that at a certain automobile plant the average number of work stoppages per day due to equipment problems during the production process is What is the approximate probability of having 15 or fewer work stoppages due to equipment problems on any given day?