Question 1

Find the mean of the set of sample data. ​
58, 62, 90, 82, 76, 60, 90
​

Accepted Answer

A) 76 
B) 74 
C) 32 
D) 82 
E) 90 
A) 76 
B) 74 
C) 32 
D) 82 
E) 90

Question 2

Suppose the Rent-to-Own Company estimates that 30% of its rentals result in a sale of the product. If the company rents 13,000 of its product in a year, what is the probability that it will sell at most 4,000 of its products? Round your answer to four decimal places. ​

Accepted Answer

A) 0.9726 
B) 0.8855 
C) 0.0274 
D) 0.6316 
E) 0.7903 
A) 0.9726 
B) 0.8855 
C) 0.0274 
D) 0.6316 
E) 0.7903

Question 3

Suppose a standardized exam for admission to a special program has been passed by 54% of the students taking it over the last five years. Suppose that 1368 of 2400 students taking the test this year pass. What is the probability that at least 1368 would pass if the pass rate is 54%? Round your answer to four decimal places. ​

Accepted Answer

A) 0.0017 
B) 0.9983 
C) 0.1072 
D) 0.2956 
E) 0.4000 
A) 0.0017 
B) 0.9983 
C) 0.1072 
D) 0.2956 
E) 0.4000

Question 4

If the probability that a newborn child is a male is   , what is the expected number of male children in a family having 2 children? Round your answer to two decimal places. ​

Accepted Answer

A) 1.50 
B) 1.13 
C) 2.00 
D) 0.50 
E) 1.00 
A) 1.50 
B) 1.13 
C) 2.00 
D) 0.50 
E) 1.00

Question 5

Suppose that AudioMart has a secret sale released only on the Internet because management thought that word-of-mouth publicity about the sale would result in 5% of U.S. households recognizing the company name. If this is true, what is the probability that at least 100 of 2000 people surveyed recognize the company name? Round your answer to four decimal places. ​

Accepted Answer

A) ​1.0199 
B) ​0.5199 
C) ​0.5258 
D) ​0.5261 
E) ​0.5249 
A) ​1.0199 
B) ​0.5199 
C) ​0.5258 
D) ​0.5261 
E) ​0.5249

Question 6

Suppose that a student is offered a chance to draw a card from an ordinary deck of 52 playing cards and win $18 for an ace, $8 for a king, and $1 for a queen. If $5 must be paid to play the game, what is the expected loss every time the game is played by the student? ​

Accepted Answer

A) expected loss $4.08 
B) expected loss $2.92 
C) expected loss $5.00 
D) expected loss $2.08 
E) expected loss $1.77 
A) expected loss $4.08 
B) expected loss $2.92 
C) expected loss $5.00 
D) expected loss $2.08 
E) expected loss $1.77

Question 7

Suppose it has been determined empirically that a certain cell will survive for a given period of time is 0.2. What is the probability that at most 280 of 1500 of these cells will survive for this period of time? Round your answer to four decimal places. ​

Accepted Answer

A) ​0.6002 
B) ​0.8928 
C) ​0.0934 
D) ​0.7515 
E) ​0.9066 
A) ​0.6002 
B) ​0.8928 
C) ​0.0934 
D) ​0.7515 
E) ​0.9066

Question 8

Find the variance of the set of sample data. ​
83, 89, 87, 99, 92, 99
​

Accepted Answer

A) 42.3 
B) 90.5 
C) 91.5 
D) 549 
E) 6.5 
A) 42.3 
B) 90.5 
C) 91.5 
D) 549 
E) 6.5

Question 9

Suppose a population of scores x is normally distributed with   and   Use the standard normal distribution to find   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.3413 
B) 0.8413 
C) 0.1587 
D) 0.6826 
E) 0.3174 
A) 0.3413 
B) 0.8413 
C) 0.1587 
D) 0.6826 
E) 0.3174

Question 10

The heights of a certain species of plant are normally distributed, with mean 22 cm and standard deviation 4 cm. What is the probability that a plant chosen at random will be will be between 18 and 26 cm tall? Round your answer to four decimal places. ​

Accepted Answer

A) 0.6826 
B) 0.3413 
C) 0.8413 
D) 0.1587 
E) 0.6587 
A) 0.6826 
B) 0.3413 
C) 0.8413 
D) 0.1587 
E) 0.6587

Question 11

Expand   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

If the ratio of boys born to girls born is 75 to 60, and if 17 children are born in a certain hospital in a day, what is the probability that 6 of them are boys? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(6 Boys) = 0.048634 
B) Pr(6 Boys) = 0.024317 
C) Pr(6 Boys) = 0.032422 
D) Pr(6 Boys) = 0.040528 
E) Pr(6 Boys) = 0.019453 
A) Pr(6 Boys) = 0.048634 
B) Pr(6 Boys) = 0.024317 
C) Pr(6 Boys) = 0.032422 
D) Pr(6 Boys) = 0.040528 
E) Pr(6 Boys) = 0.019453

Question 13

Suppose that 30% of the patients who have a certain disease die from it. If 13 patients have the disease, what is the probability that no more than 4 patients will die from it? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(Deaths  
4) = 0.308168 
B) Pr(Deaths  
4) = 0.192789 
C) Pr(Deaths  
4) = 0.356936 
D) Pr(Deaths  
4) = 0.898811 
E) Pr(Deaths  
4) = 0.451835 
A) Pr(Deaths  
4) = 0.308168 
B) Pr(Deaths  
4) = 0.192789 
C) Pr(Deaths  
4) = 0.356936 
D) Pr(Deaths  
4) = 0.898811 
E) Pr(Deaths  
4) = 0.451835

Question 14

A bag contains 5 red balls and 2 black balls. We draw 5 balls, with each one replaced before the next is drawn. What is the probability that 3 balls drawn will be red? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(3 Red) = 0.600000 
B) Pr(3 Red) = 0.014875 
C) Pr(3 Red) = 0.297495 
D) Pr(3 Red) = 0.002479 
E) Pr(3 Red) = 0.578330 
A) Pr(3 Red) = 0.600000 
B) Pr(3 Red) = 0.014875 
C) Pr(3 Red) = 0.297495 
D) Pr(3 Red) = 0.002479 
E) Pr(3 Red) = 0.578330

Question 15

A company produces shotgun shells in batches of 100. A sample of 5 is tested from each batch, and if more than one defect is found, the entire batch is tested. If 4% of the shells are actually defective, what is the probability of more than 1 defective shell in a batch of 5? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(>1 Defect) = 0.002000 
B) Pr(>1 Defect) = 0.169869 
C) Pr(>1 Defect) = 0.014156 
D) Pr(>1 Defect) = 0.014758 
E) Pr(>1 Defect) = 0.008000 
A) Pr(>1 Defect) = 0.002000 
B) Pr(>1 Defect) = 0.169869 
C) Pr(>1 Defect) = 0.014156 
D) Pr(>1 Defect) = 0.014758 
E) Pr(>1 Defect) = 0.008000

Question 16

Suppose the Circuitown buys plasma televisions in sets of 1500. If a television is defective with probability 0.01, what is the probability that at least 24 televisions will be defective in a set? Round your answer to four decimal places. ​

Accepted Answer

A) 0.9864 
B) 0.0136 
C) 0.8821 
D) 0.7496 
E) 0.809 
A) 0.9864 
B) 0.0136 
C) 0.8821 
D) 0.7496 
E) 0.809

Question 17

Suppose that the duration of the mating calls of a population of tree toads are normally distributed, with mean 188 milliseconds (msec) and standard deviation 40 msec. What proportion of these calls would be expected to last between 192 and 268 msec? Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A) 0.5626 
B) 0.9374 
C) 0.4374 
D) 0.1874 
E) 0.1750 
A) 0.5626 
B) 0.9374 
C) 0.4374 
D) 0.1874 
E) 0.1750

Question 18

Forty-nine percent of accountants taking a CPA exam fail the first time. If 1000 candidates take the exam for the first time, what is the expected number that will pass? ​

Accepted Answer

A) 951 accountants 
B) 949 accountants 
C) 851 accountants 
D) 490 accountants 
E) 510 accountants 
A) 951 accountants 
B) 949 accountants 
C) 851 accountants 
D) 490 accountants 
E) 510 accountants

Question 19

Suppose a fair die is rolled 13 times. What is the probability that 1 "aces" (1's) will occur? Round your answer to six digital places. ​

Accepted Answer

A) Pr(1 Aces) = 0.033399 
B) Pr(1 Aces) = 0.001587 
C) Pr(1 Aces) = 0.000016 
D) Pr(1 Aces) = 0.000000 
E) Pr(1 Aces) = 0.243006 
A) Pr(1 Aces) = 0.033399 
B) Pr(1 Aces) = 0.001587 
C) Pr(1 Aces) = 0.000016 
D) Pr(1 Aces) = 0.000000 
E) Pr(1 Aces) = 0.243006

Question 20

A multiple-choice test has 28 questions and 3 choices for each question. If a student is totally unprepared and guesses on each question, what is the probability that she will answer 15 questions correctly? Round your answer to four decimal places. ​

Accepted Answer

A) 0.0067 
B) 0.0134 
C) 0.0089 
D) 0.0149 
E) 0.0206 
A) 0.0067 
B) 0.0134 
C) 0.0089 
D) 0.0149 
E) 0.0206

Find the mean of the set of sample data. 58, 62, 90, 82, 76, 60, 90

Suppose the Rent-to-Own Company estimates that 30% of its rentals result in a sale of the product. If the company rents 13,000 of its product in a year, what is the probability that it will sell at most 4,000 of its products? Round your answer to four decimal places.

If the probability that a newborn child is a male is , what is the expected number of male children in a family having 2 children? Round your answer to two decimal places.

Suppose that a student is offered a chance to draw a card from an ordinary deck of 52 playing cards and win $18 for an ace, $8 for a king, and $1 for a queen. If $5 must be paid to play the game, what is the expected loss every time the game is played by the student?

Suppose it has been determined empirically that a certain cell will survive for a given period of time is 0.2. What is the probability that at most 280 of 1500 of these cells will survive for this period of time? Round your answer to four decimal places.

Find the variance of the set of sample data. 83, 89, 87, 99, 92, 99

Suppose a population of scores x is normally distributed with and Use the standard normal distribution to find . Round your answer to four decimal places.

The heights of a certain species of plant are normally distributed, with mean 22 cm and standard deviation 4 cm. What is the probability that a plant chosen at random will be will be between 18 and 26 cm tall? Round your answer to four decimal places.

Expand

If the ratio of boys born to girls born is 75 to 60, and if 17 children are born in a certain hospital in a day, what is the probability that 6 of them are boys? Round your answer to six decimal places.

Suppose that 30% of the patients who have a certain disease die from it. If 13 patients have the disease, what is the probability that no more than 4 patients will die from it? Round your answer to six decimal places.

A bag contains 5 red balls and 2 black balls. We draw 5 balls, with each one replaced before the next is drawn. What is the probability that 3 balls drawn will be red? Round your answer to six decimal places.

Suppose the Circuitown buys plasma televisions in sets of 1500. If a television is defective with probability 0.01, what is the probability that at least 24 televisions will be defective in a set? Round your answer to four decimal places.

Forty-nine percent of accountants taking a CPA exam fail the first time. If 1000 candidates take the exam for the first time, what is the expected number that will pass?

Suppose a fair die is rolled 13 times. What is the probability that 1 "aces" (1's) will occur? Round your answer to six digital places.

A multiple-choice test has 28 questions and 3 choices for each question. If a student is totally unprepared and guesses on each question, what is the probability that she will answer 15 questions correctly? Round your answer to four decimal places.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 9: Further Topics in Probability; Data Description

Find the mean of the set of sample data. ​ 58, 62, 90, 82, 76, 60, 90 ​