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

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

Exam 6: The Binomial Probability Distribution and Related Topics

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?

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Question 1

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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.

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Question 2

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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. Age range (yr) - - - - - - + Midpoint (x) 24.5 34.5 44.5 54.5 64.5 75.5 84.5 Percent of nurses 5.7\% 9.7\% 19.5\% 29.2\% 25.0\% 9.1\% 1.8\%

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Question 3

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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. x= age 5 6 7 8 9 P (accident) 0.01182 0.01282 0.01386 0.01513 0.01602

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Question 4

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.

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Question 5

Give an example of a continuous random variable.

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Question 6

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.

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Question 7

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.

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Question 8

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?

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Question 9

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. $r \geq 2$

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Question 10

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.

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Question 11

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.

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Question 12

Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Make a histogram for the probability distribution. Age range (y) - - - - - - + Midpoint (x) 24.5 34.5 44.5 54.5 64.5 75.5 84.5 Percent of nurses 9.8\% 5.6\% 19.4\% 24.9\% 29.3\% 9.3\% 1.7\%

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Question 13

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. $\mathcal { \sigma }$ Age range (yr) - - - - - - + Midpoint (x) 24.5 34.5 44.5 54.5 64.5 75.5 84.5 Percent of nurses 5.8\% 9.8\% 19.6\% 29.2\% 25.1\% 9.1\% 1.4\%

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Question 14

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.

(Multiple Choice)

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Question 15

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: x= age 5 6 7 8 9 P (accident) 0.01191 0.01292 0.01396 0.01503 0.01613 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.

(Multiple Choice)

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Question 16

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.

(Multiple Choice)

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Question 17

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. x= age 5 6 7 8 9 P (accident) 0.01182 0.01282 0.01386 0.01513 0.01602

(Multiple Choice)

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Question 18

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.

(Multiple Choice)

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Question 19

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. $r < 3$

(Multiple Choice)

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Question 20

Showing 1 - 20 of 38

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?

Give an example of a continuous random variable.

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.

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.

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?

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.

Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Make a histogram for the probability distribution. Age range (y) - - - - - - + Midpoint (x) 24.5 34.5 44.5 54.5 64.5 75.5 84.5 Percent of nurses 9.8\% 5.6\% 19.4\% 24.9\% 29.3\% 9.3\% 1.7\%

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