# Mathematics

Question 1

1. Find the indicated probability. A sample space consists of 174 separate events that are equally likely. What is the probability of each?

0

1

174

1/174

Question 2

1. From the information provided, create the sample space of possible outcomes. Flip a coin twice.

HH, TT, HT, HT

HH, HT, TH, TT

HT, TH

HH, HT, TT

Question 3

1. Find the indicated probability. A spinner has equal regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3?

2/3

10/9

17

1/3

Question 4

1. Find the indicated probability. Round to the nearest thousandth. A study conducted at a certain college shows that 55% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

0.550

0.996

0.143

0.985

Question 5

1. Evaluate the expression. 4!

28

20

6

24

Question 6

1. Solve the problem. How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

720

48

20,160

40,320

Question 7

Find the mean of the given probability distribution. Choose A, B, C, or D

x / P(x)

0 0.42

1 0.12

2 0.34

3 0.05

4 0.07

Question 8

1. Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Find the probability of selecting exactly 8 girls.

0.183

0.022

0.122

0.000

Question 9

1. Provide an appropriate response. In a game, you have a 1/36 probability of winning $94 and a 35/36 probability of losing $8. What is your expected value?

$10.39

-$5.17

-$7.78

$2.61

Question 10

1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 57 times, keeping track of the numbers that are rolled.

Not binomial: there are too many trials.

Not binomial: the trials are not independent.

Procedure results in a binomial distribution.

Not binomial: there are more than two outcomes for each trial.

Question 11

1. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 5, x = 2, p = 0.70

0.464

0.198

0.700

0.132

Question 12

1. Find the indicated probability. Round to three decimal places. A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

0.828

0.172

0.205

0.377

Question 13

1. Find the standard deviation, , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 21; p = 0.2

1.83

5.95

5.10

-0.58

Question 14

1. Use the Poisson Distribution to find the indicated probability. If the random variable x has a Poisson Distribution with mean 6, find the probability that x = 2.

0.05577

0.04462

0.12128

0.01487

Question 15

1. Use the Poisson model to approximate the probability. Round your answer to four decimal places. Suppose the probability of a major earthquake on a given day is 1 out of 15,000. Use the Poisson distribution to approximate the probability that there will be at least one major earthquake in the next 2000 days.

0.1248

0.0081

0.8752

0.8833

0.1167

Question 16

1. Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.523, n = 25

Critical values: r = ±0.487, significant linear correlation

Critical values: r = ±0.396, no significant linear correlation

Critical values: r = ±0.396, significant linear correlation

Critical values: r = ±0.487, no significant linear correlation