Practice Set Assignment
1. List the simple events for each of the following statistical experiments in a sample space.
a) One roll of a die.
Note: Separate your response with a comma (,). For example 22, 23, 24
b) Three tosses of a coin.
Note: Use this notation for your answer. heads = H. tails = T. For example HT, TH
c) One toss of a coin and one roll of a die.
Note: Use this notation. Heads = H or numbers 1, 2, 3, 4, 5, 6 for the dice. For example
H1 indicates heads and dice roll equal to 1.
2. Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. Indicate which are simple and which are compound events.
a) Both students suffer from math anxiety.
b) Exactly one student suffers from math anxiety.
c) The first student does not suffer and the second suffers from math anxiety.
d) None of the students suffers from math anxiety.
3. A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat.
a) What is the probability that this marble is red (round to two decimal places)?
b) What is the probability that this marble is green (round to two decimal places?
4. Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses.
|
Have Shopped
|
Have Never Shopped
|
|
Male
|
500
|
700
|
|
Female
|
300
|
500
|
a) If one adult is selected at random from these 2000 adults, find the probability that this adult has never shopped on the Internet.
b) If one adult is selected at random from these 2000 adults, find the probability that this adult is a male.
c) If one adult is selected at random from these 2000 adults, find the probability that this adult has shopped on the Internet given that this adult is a female.
d) If one adult is selected at random from these 2000 adults, find the probability that this adult is a male given that this adult has never shopped on the Internet.
5. Find the joint probability of AA and BB for the following.
a) P(A)=.36 and P(B|A)=.87
b) P(B)=.53 and P(A|B)=.22
6. Classify each of the following random variables as discrete or continuous.
a) The time left on a parking meter
b) The number of bats broken by a major league baseball team in a season
c) The number of cars in a parking lot at a given time
d) The price of a car
e) The number of cars crossing a bridge on a given day
f) The time spent by a physician examining a patient
g) The number of books in a student's bag
7. The following table gives the probability distribution of a discrete random variable x.
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
|
P(x)
|
.11
|
.19
|
.28
|
.15
|
.12
|
.09
|
.06
|
Find the following probabilities.
a) P(1≤x≤4)
b) Probability that x assumes a value less than 4.
c) Probability that x assumes a value greater than 2.
8. A limousine has eight tires on it. A fleet of such limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the probability distribution of the number of defective tires on this fleet of limos where xx represents the number of defective tires on a limo and P(x) is the corresponding probability.
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
P(x)
|
.0454
|
.1723
|
.2838
|
.2669
|
.1569
|
.0585
|
.0139
|
.0015
|
.0008
|
Calculate the mean and standard deviation of this probability distribution. Give a brief interpretation of the values of the mean and standard deviation.
9. Let xx be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities.
a) p(5) for n=8 and p=.70
b) p(3) for n=4 and p=.40
Verify your answers by using Table I of Appendix B.
10. Let x be a discrete random variable that possesses a binomial distribution.If n = 5 and p = 0.8, then...
a) What is the mean (round to three decimal places)
b) What is the standard deviation of the probability distribution (round to three decimal places)?