IT College

Introduction to Computer Statistical Packages

Eng. Heba Hamad2009

Examples ofBinomial Probability Distributions

Example 1There is a 0.54 probability that a randomly selected freshman at a two-year college will return the second year. In each case, assume that 5 freshmen at a two-year college are randomly selected and find the probability indicated

• Find the probability that at least four of the freshmen return for the second year

• Find the probability that at most two of the freshmen return for the second year

• Find the probability that more than one of the freshmen return for the second year

Solution:

0555

1445 46.054.046.054.0

)5()4(

CC

PP

)2()1()0( PPP

)5()4()3()2( PPPP

Example 2The rate of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80% of its flights arriving on time. A test is conducted by randomly selecting 15 southwest flights and observing whether they arrive on time.

• Find the probability that exactly 10 flights arrive on time

• Find the probability that at least 10 flights arrive late

Solution:

5101015 2.08.0)10( CP

)15()14()13()12()11()10( PPPPPP

)5()4()3()2()1()0( PPPPPP

Where success = arrive late

OR

Where success = arrive on time

Example 3

Nine Percent of men and 0.25% of women cannot distinguish between the colors red and green. This is a type of color blindness that cause problems with traffic signals. If 6 men are randomly selected for a study of traffic signals perceptions, find the probability that exactly two of them cannot distinguish between red and green.

Solution:

4226 91.0*09.0)2( CP

0833.0)2( P

In a housing study, it was found that 26% of college students live in campus housing. The providence Insurance Company wants to sell those students special policies insuring their personal property. If they test a marketing strategy by randomly selecting six college students,

• what is the probability that at least one of them live in campus housing

• what is the mean of no. of students live in campus housing

Example 4

Air America has a policy of booking as many as 15 persons on an airplane that can seat only 14. Because past studies have revealed that only 85% of the booked passengers actually arrive for the flight. Find the Probability that if Air America books 15 persons, not enough seats will be available.

Example 5

An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 14 of these cars are independently sampled, what is the probability that more than 11 cars need new gas tanks?

Example 6

There are five flights daily from Pittsburgh via US airways into the Bradford, Pennsylvania Regional Airport. Suppose the probability that any flight arrives late is 0.2. what is the probability that none of the flights are late today? What is the probability that exactly one of the flights is late today?

Example 7

Suppose 60 percent of people prefer Coke to Pepsi. We select 18 people for further study.

• How many would you expect to prefer Coke ?

• What is the probability 10 of those surveyed will prefer Coke ?

• What is the probability 15 prefer Coke ?

• Compute the mean and the standard deviation

Example 8

In a recent study 90% of the homes in the United States were found to have large screen TVs. In a sample of nine homes, what is the probability that:

• All nine have large screen TVs

• Less than five have large screen TVs

• More than five have large screen TVs

• at least seven homes have large screen TVs

Example 9

A company receive 60% of its order over the internet. Within a collection of 18 independently placed orders. What is the probability that:

• Between eight and ten (inclusive) of the orders are received over the internet

• no more than four of the orders are received over the internet

Example 10