Deck 6: The Binomial Probability Distribution and Related Topics

Question 1

The Honolulu Advertiser stated that in Honolulu there was an average of 665 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 322 homes. Let r be the number of homes that will be burglarized in a year. Compute the probability for . Round your answer to the nearest ten thousandth. $r < 3$

A)0.9834
B)0.9982
C)0.9004
D)0.9856
E)0.9964

Answer 1

0.9856

Question 2

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $39. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 31 cookies. What is the probability she will win the dinner for two? Write your answer as a fraction in simplest form, if one exists.

A) $\frac { 31 } { 687 }$
B) $\frac { 687 } { 718 }$
C) $\frac { 31 } { 718 }$
D) $\frac { 1 } { 31 }$
E)none of these choices

Answer 2

$\frac { 31 } { 718 }$

Question 3

Compute the expected age $\mu$ of a British nurse in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth. $$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Age range (yr) } & \mathbf { 2 0 } - \mathbf { 2 9 } & \mathbf { 3 0 } - \mathbf { 3 9 } & \mathbf { 4 0 } - \mathbf { 4 9 } & \mathbf { 5 0 } - \mathbf { 5 9 } & \mathbf { 6 0 - 6 9 } & \mathbf { 7 0 } - \mathbf { 7 9 } & \mathbf { 8 0 } + \\\hline \text { Midpoint } ( x ) & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 & 75.5 & 84.5 \\\hline \text { Percent of nurses } & 5.6 \% & 9.8 \% & 19.4 \% & 29.2 \% & 25.1 \% & 9.1 \% & 1.8 \% \\\hline\end{array}$$

A)54.50
B)59.50
C)53.85
D)53.88
E)43.88

Answer 3

53.88

Question 4

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $60,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $800 above the expected total losses of $4179, how much should it charge for the policy?
$$\begin{array} { l c c c c c } x = \text { age } & 5 & 6 & 7 & 8 & 9 \\P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602\end{array}$$

A)$4977
B)$4969
C)$4989
D)$4979
E)$4981

Question 5

The Honolulu Advertiser stated that in Honolulu there was an average of 651 burglaries per 500,000 households in a given year. In the Kohola Drive neighborhood there are 317 homes. Let r be the number of homes that will be burglarized in a year. Compute the probability for . Round your answer to the nearest ten thousandth. $r = 3$

A)0.0011
B)0.0029
C)0.0383
D)0.0183
E)0.0072

Question 6

Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 5 questions, find the probability that he will answer all questions correctly. Round your answer to the nearest thousandth.

A)0.004
B)0.333
C)0.500
D)0.067
E)0.600

Question 7

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Find the probability that a British nurse selected at random in 1851 would be 30 years of age or older. Round your answer to nearest thousandth. $$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Age range (yr) } & \mathbf { 2 0 } - \mathbf { 2 9 } & \mathbf { 3 0 } - \mathbf { 3 9 } & \mathbf { 4 0 } - \mathbf { 4 9 } & \mathbf { 5 0 } - \mathbf { 5 9 } & \mathbf { 6 0 } - \mathbf { 6 9 } & \mathbf { 7 0 } - \mathbf { 7 9 } & \mathbf { 8 0 } + \\\hline \text { Midpoint } ( x ) & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 & 75.5 & 84.5 \\\hline \text { Percent of nurses } & 5.7 \% & 9.7 \% & 19.5 \% & 29.2 \% & 25.0 \% & 9.1 \% & 1.8 \% \\\hline\end{array}$$

A)0.097
B)0.098
C)0.943
D)0.292
E)0.942

Question 8

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $31. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 723 cookies before the drawing. Lisa bought 25 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. How much did she effectively contribute to the hiking club?

A)$21.89
B)$70.73
C)$73.93
D)$23.76
E)$23.93

Question 9

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: Jim is applying to a car insurance company for his car insurance policy. The expected loss to the car insurance company for the 5th, 6th, 7th, 8th, and 9th years would be $595.50, $646.00, $698.00, $751.50 or $806.50 respectively. What would be the total expected loss to the car insurance company over the years 5 through 9? Round your answer to the nearest dollar.
$$\begin{array} { l c c c c c } x = \text { age } & 5 & 6 & 7 & 8 & 9 \\P \text { (accident) } & 0.01191 & 0.01292 & 0.01396 & 0.01503 & 0.01613\end{array}$$

A)$3496
B)$3497
C)$3498
D)$3499
E)$3495

Question 10

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $37. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 725 cookies before the drawing. Lisa bought 27 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.

A)$1.43
B)$1.37
C)$35.62
D)$1.38
E)$37.00

Question 11

Richard has been given an 11-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. What is considered the success?

A)number of questions
B)Richard answers a question correctly.
C)number of questions answered
D)Richard is unable to answer a question correctly.
E)none of the choices

Question 12

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: Jim is applying to a car insurance company for his car insurance policy. If the car insurance company charges $7000 for the policy, how much profit does the company expect to make? Round your answer to the nearest dollar.
$$\begin{array} { l c c c c c } x = \text { age } & 5 & 6 & 7 & 8 & 9 \\P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602\end{array}$$

A)$3515
B)$3520
C)$3513
D)$3522
E)$3518

Question 13

Give an example of a continuous random variable.

A)The number of fish caught by a fishing boat
B)The number of coins contained in a slot machine
C)The number of traffic accidents in a city
D)The number of gallons of water in a reservoir
E)The number of tables sold at a furniture store

Question 14

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $30,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $600 above the expected total losses, how much should it charge for the policy? Round your answer to the nearest dollar.
$$\begin{array} { l c c c c c } x = \text { age } & 5 & 6 & 7 & 8 & 9 \\P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602\end{array}$$

A)$2688
B)$2690
C)$2692
D)$2685
E)$2683

Question 15

Compute the standard deviation for ages of British nurses in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth. $$\mathcal { \sigma }$$ $$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Age range (yr) } & \mathbf { 2 0 } - \mathbf { 2 9 } & \mathbf { 3 0 } - \mathbf { 3 9 } & \mathbf { 4 0 } - \mathbf { 4 9 } & \mathbf { 5 0 } - \mathbf { 5 9 } & \mathbf { 6 0 } - \mathbf { 6 9 } & \mathbf { 7 0 } - \mathbf { 7 9 } & \mathbf { 8 0 } + \\\hline \text { Midpoint } ( x ) & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 & 75.5 & 84.5 \\\hline \text { Percent of nurses } & 5.8 \% & 9.8 \% & 19.6 \% & 29.2 \% & 25.1 \% & 9.1 \% & 1.4 \% \\\hline\end{array}$$

A)13.57
B)1.52
C)3.26
D)53.68
E)17.26

Question 16

Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Make a histogram for the probability distribution. $$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Age range (y) } & \mathbf { 2 0 } - \mathbf { 2 9 } & \mathbf { 3 0 } - \mathbf { 3 9 } & \mathbf { 4 0 } - \mathbf { 4 9 } & \mathbf { 5 0 } - \mathbf { 5 9 } & \mathbf { 6 0 } - \mathbf { 6 9 } & \mathbf { 7 0 } - \mathbf { 7 9 } & \mathbf { 8 0 } + \\\hline \text { Midpoint } ( x ) & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 & 75.5 & 84.5 \\\hline \text { Percent of nurses } & 9.8 \% & 5.6 \% & 19.4 \% & 24.9 \% & 29.3 \% & 9.3 \% & 1.7 \% \\\hline\end{array}$$

A)
B)
C)
D)
E)

Question 17

The Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 300,000 households in a given year. In the Kohola Drive neighborhood there are 323 homes. Let r be the number of homes that will be burglarized in a year. Compute the probability for . Round your answer to the nearest ten thousandth. $r \geq 2$

A)0.1669
B)0.0341
C)0.4082
D)0.1558
E)0.0369

Question 18

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $30,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: $$\begin{array} { l c c c c c } x = \text { age } & 5 & 6 & 7 & 8 & 9 \\P \text { (accident) } & 0.01191 & 0.01292 & 0.01396 & 0.01503 & 0.01613\end{array}$$ Jim is applying to a car insurance company for his car insurance policy. If the car insurance company charges $6000 for the policy and the expected total loss is $2099, how much profit does the company expect to make? Round your answer to the nearest dollar.

A)$3902
B)$3905
C)$3900
D)$3897
E)$3903

Question 19

Give an example of a discrete random variable.

A)The number of inches of rainfall in a county
B)The number of beverages sold at a lemonade stand
C)The number of gallons of concrete used at a construction site
D)The time required for a runner to finish a marathon
E)The temperature of a pot roast cooking in an oven

Question 20

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 32 cookies. What is the probability she will not win the dinner for two? Write your answer as a fraction in simplest form, if one exists.

A) $\frac { 16 } { 343 }$
B) $\frac { 343 } { 359 }$
C) $\frac { 16 } { 359 }$
D) $\frac { 1 } { 32 }$
E)none of these choices

Question 21

The probability of a radar station detecting an enemy plane is 0.55 and the probability of not detecting an enemy plane is 0.45. If 5 stations are in use, what is the standard deviation? Round your answer to nearest hundredth.

A)1.66
B)1.11
C)1.24
D)2.75
E)none of these choices

Question 22

Richard has been given a 7-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 7 questions, find the probability that he will answer at least 6 questions correctly. Round your answer to the nearest thousandth.

A)0.006
B)0.007
C)0.857
D)0.286
E)0.500

Question 23

There are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution. $$\begin{array} { | c | c | } \hline \boldsymbol { r } & P ( r ) \\\hline 0 & 0.041 \\\hline 1 & 0.200 \\\hline 2 & 0.368 \\\hline 3 & 0.300 \\\hline 4 & 0.092 \\\hline\end{array}$$

A)
B)
C)
D)
E)

Question 24

Suppose that on the leeward side of the island of Oahu, in the small village of Nanakuli, about 30% of the residents are of Hawaiian ancestry. Let 1, 2, 3,… represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli. Compute the probability for 2. Round your answer to the nearest ten thousandth. $n =$ $n \geq$

A)0.6900
B)0.1000
C)0.0900
D)0.7000
E)0.3480

Question 25

The probability of a radar station detecting an enemy plane is 0.85. If 60 stations are in use, what is the expected number of stations that will detect an enemy plane?

A)60
B)51
C)0
D)58
E)none of these choices

Question 26

Richard has been given a 10-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 10 questions, find the probability that he will answer at least 6 questions correctly. Round your answer to the nearest thousandth.

A)0.057
B)0.500
C)0.600
D)0.200
E)0.077

Question 27

There are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.

A)
B)
C)
D)
E)

Question 28

There are 6 radar stations and the probability of a single radar station detecting an enemy plane is 0.40. Identify the type of histogram for the probability distribution.

A)uniform or rectangular
B)none of these choices
C)skewed left
D)symmetric
E)skewed right

Question 29

Richard has been given a 7-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 7 questions, find the probability that he will answer all questions incorrectly. Round your answer to the nearest thousandth.

A)0.750
B)0.500
C)0.540
D)0.133
E)0.857

Question 30

There are 6 radar stations and the probability of a single radar station detecting an enemy plane is 0.35. Identify the type of histogram for the probability distribution.

A)skewed left
B)symmetric
C)uniform or rectangular
D)none of these choices
E)skewed right

Question 31

There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.65. What is the probability of 3 stations detecting an enemy plane? Round your answer to nearest hundredth.

A)0.01
B)0.65
C)0.12
D)0.34
E)0.03

Question 32

Richard has been given a 10-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 10 questions, find the probability that he will answer no more than 2 questions correctly. Round your answer to the nearest thousandth.

A)0.282
B)0.200
C)0.526
D)0.050
E)0.500

Question 33

There are 3 radar stations and the probability of a single radar station detecting an enemy plane is 0.65 and the probability of not detecting an enemy plane is 0.35. What is the probability that the number of stations that detect a plane is no more than 2? Round your answer to nearest hundredth.

A)0.73
B)0.44
C)0.65
D)0.16
E)0.15

Question 34

Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 5 questions, find the probability that he will answer all questions correctly. Round your answer to the nearest thousandth.

A)0.004
B)0.333
C)0.500
D)0.067
E)0.600

Question 35

The probability of a radar station detecting an enemy plane is 0.85. If 7 stations are in use, what is the standard deviation? Round your answer to nearest hundredth.

A)2.44
B)0.94
C)0.89
D)5.95
E)none of these choices

Question 36

Richard has been given an 11-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 11 questions, find the probability that he will answer all questions incorrectly. Round your answer to the nearest thousandth.

A)0.800
B)0.086
C)0.621
D)0.909
E)0.500

Question 37

The probability of a radar station detecting an enemy plane is 0.65 and the probability of not detecting an enemy plane is 0.35. If 20 stations are in use, what is the expected number of stations that will detect an enemy plane?

A)20
B)0
C)18
D)13
E)none of these choices

Question 38

Richard has been given a 12-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 12 questions, find the probability that he will answer no more than 3 questions correctly. Round your answer to the nearest thousandth.

A)0.258
B)0.500
C)0.250
D)0.649
E)0.063