Show all work and formulas.
1) [5 points]. Professor Kwizz used her previous years attendance records from her statistics class of 32
students to construct the following probability distribution. The table lists the number of people absent on an
exam day and its assigned probability.
X P(X)
1 0.15
2 0.25
3 0.2
4 0.15
5 0.05
6 0.1
7 0.05
8 0.05
a) What is the probability that between 3 and 5 students, inclusive, are absent on exam day?
b) On average how many students would you expect to be absent on an exam day?
2) [4 points]. A recent report shows that 80% of elementary school teachers have a computer at home. 12
elementary school teachers are randomly selected. You may assume this situation follows a binomial
distribution. Find the probability that at most 6 of them have a home computer.
3) [4 points]. A software company sells software on the Internet. The number of unsolicited sales follows a
Poisson distribution with a mean of 5 sales per day. What is the probability the company makes at least 1 sale
in one day?
4) [5 points]. According to the 1998 Health and Human Service’s National Household Survey on Drug Abuse,
18% of children between the ages of 12 and 17 are cigarette smokers. If 8 children in this age group are
selected randomly find the probability that 2 of them are cigarette smokers. You may assume this is a binomial
probability.
5) [10 points]. According to the manufacturer of Crackle natural peach flavored iced tea drinks, the net amount
of iced tea in a glass bottle is normally distributed with a mean of 12 ounces and a standard deviation of 0.018
ounces. You randomly select one bottle of iced tea this company produced. You may assume this situation is
normally distributed.
a) What is the probability that it has less than 11.98 ounces in it?
b) What is the probability that it has between 11.96 ounces and 12.02 ounces, inclusive, in it?
6) [10 points]. It is claimed that 25% of Americans have cellular phones. A survey of 440 Americans is
conducted. You may assume this binomial distribution is approximately normally distributed.
a) Calculate the mean and standard deviation of this distribution.
7) [4 points]. The heights of 12-month-old boys are approximately normally distributed with a mean of 29.8
inches and a standard deviation of 1.2 inches.
a) What height separates the shortest 20% of 12-month-old boys from the rest?
b) What height separates the tallest 30% of 12-month-old boys from the rest?
REFERENCE FORMULAS
Discrete Probability Distributions
a) Mean  = (x • P(x))
b) Standard Deviation (( ) ( )) 2  =  x − •P x
Binomial Probability Formula
( ) (1 ) n x n x P X C p p x
−
= −
Binomial Probability Distributions
a) Mean
 = np
b) Standard Deviation  = np(1− p)
Poisson Probability Formula
!
( )
x
e
P x
x



•

−
z-scores for the Normal Distribution


− 

x
z
Using z-scores to find values for given probabilities
x z = +  

Sample Solution