Chapter 5-2-4
Review
Name:___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the given random variable as being discrete or continuous.
1) The cost of a randomly selected orange
2) The height of a randomly selected student
3) The pH level in a shampoo
Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
4)
x P(x)
0 0.49
1 0.05
2 0.32
3 0.07
4 0.07
Find the mean of the given probability distribution.
5) The number of points scored in a domino tournament on a typical scoring play has the following probability
distribution.
x
5 10 15 20 25 0
p(x) 0.04 0.11 0.30 0.29 0.21 .05
6) The accompanying table shows the probability distribution for x, the number that shows up when a loaded die
is rolled.
x P(x)
1 0.12
2 0.12
3 0.12
4 0.12
5 0.11
6 0.41
Solve the problem.
7) In a game, you have a 1/20 probability of winning $136 and a 19/20 probability of losing $5. what is your
expected value?
8) A 28-year-old man pays $206 for a one-year life insurance policy with coverage of $60,000. If the probability
that he will live through the year is 0.9994, what is the expected value for the insurance policy?
Find the mean for the random variable.
9) A batch of 18 light bulbs includes 5 that are defective. Two light bulbs are randomly selected without
replacement. If the random variable x represents the number of defective light bulbs selected, find the mean for
the random variable x.
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Find the mean or standard deviation for the random variable.
10) A class includes 4 left-handed students and 26 right-handed students. Two different students are randomly
selected. If the random variable x represents the number of left-handed students selected, find the variance for
the random variable x.
Determine whether the experiment is a binomial experiment. If it is not a binomial experiment, state the reason why.
11) Choosing 5 people (without replacement) from a group of 34 people, of which 15 are women, keeping track of
the number of men chosen.
12) Choosing 9 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement,
keeping track of the number of red marbles chosen.
Find the indicated probability.
13) What is the probability that 4 rolls of a fair die will show three fours?
14) A multiple choice test has 30 questions, and each has five possible answers, of which one is correct. If a student
guesses on every question, find the probability of getting exactly 40% correct.
15) A test consists of 10 true/false questions. To pass the test a student must answer at least 8 questions correctly. If
a student guesses on each question, what is the probability that the student will pass the test?
16) A car insurance company has determined that 4% of all drivers were involved in a car accident last year.
Among the 11 drivers living on one particular street, 3 were involved in a car accident last year. If 11 drivers are
randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard
deviations. That is, unusual values are either less than µ - 2 or greater than µ + 2 .
17) The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose
that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of
800 to contain 455 jawbreakers that weigh more than .4 ounces?
Solve the problem.
18) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 20. Find the mean
and standard deviation for the number of seeds germinating in each batch. Find the minimum and maximum
usual values. Would it be unusual for 5 seeds to germinate?
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