Question 1

Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds. {Diet Narrative} What proportion of the dieters lost more than 12 pounds?

Accepted Answer

The answer of Diet Researchers studying the effects of a...

Question 2

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability that the subway arrives in the first minute and a half?

Accepted Answer

The answer of Subway Waiting Time At a subway station...

Question 3

{Electronics Test Narrative} Find the probability that a student will take exactly one hour to finish the test.

Accepted Answer

The answer of {Electronics Test Narrative} Find the probability that...

Question 4

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

Accepted Answer

The answer of Battery Life A certain brand of batteries...

Question 5

{Electronics Test Narrative} Find the probability that a student will take more than 60 minutes to finish the test.

Accepted Answer

The answer of {Electronics Test Narrative} Find the probability that...

Question 6

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait exactly one hour?

Accepted Answer

The answer of Waiting Time The length of time patients...

Question 7

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

Accepted Answer

The answer of Battery Life A certain brand of batteries...

Question 8

{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

Accepted Answer

The answer of {Electronics Test Narrative} What is the mean...

Question 9

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. {Electronics Test Narrative} What is the probability density function for this uniform distribution?

Accepted Answer

The answer of Electronics Test The time it takes a...

Question 10

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What lifetime should the manufacturer advertise for these batteries in order that only 2% of the lamps will wear out before the advertised lifetime?

Accepted Answer

The answer of Battery Life A certain brand of batteries...

Question 11

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

Accepted Answer

The answer of Subway Waiting Time At a subway station...

Question 12

{Electronics Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test.

Accepted Answer

The answer of {Electronics Test Narrative} Find the probability that...

Question 13

The time required to complete a particular assembly operation has a uniform distribution between 25 and 50 minutes. 
 a. What is the probability density function for this uniform distribution? 
 b. What is the probability that the assembly operation will require more than 40 minutes to complete? 
 c. Suppose more time was allowed to complete the operation, and the values of X were extended to the range from 25 to 60 minutes. What would f(x)be in this case?

Accepted Answer

The answer of The time required to complete a particular...

Question 14

Suppose f(x)equals 1\50 on the interval [0, 50]. 
 a. What is the distribution of X ? 
 b. What does the graph of f(x)look like? 
 c. Find P ( X £ 25)
 d. Find P ( X ³ 25)
 e. Find P ( X = 25)
 f. Find P (0 X 
 g. Find P ( - 3 X 
 h. Find P (0 X

Accepted Answer

The answer of Suppose f(x)equals 1\50 on the interval [0,...

Question 15

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour?

Accepted Answer

The answer of Waiting Time The length of time patients...

Question 16

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the median waiting time for this subway?

Accepted Answer

The answer of Subway Waiting Time At a subway station...

Question 17

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last for more than 4,000 hours?

Accepted Answer

The answer of Battery Life A certain brand of batteries...

Question 18

{Electronics Test Narrative} What is the median amount of time it takes a student to finish the test?

Accepted Answer

The answer of {Electronics Test Narrative} What is the median...

Question 19

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours?

Accepted Answer

The answer of Waiting Time The length of time patients...

Question 20

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability density function for this uniform distribution?

Accepted Answer

The answer of Subway Waiting Time At a subway station...

Quiz 7: Continuous Probability Distributions

Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds. {Diet Narrative} What proportion of the dieters lost more than 12 pounds?

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability that the subway arrives in the first minute and a half?

{Electronics Test Narrative} Find the probability that a student will take exactly one hour to finish the test.

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

{Electronics Test Narrative} Find the probability that a student will take more than 60 minutes to finish the test.

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait exactly one hour?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. {Electronics Test Narrative} What is the probability density function for this uniform distribution?

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

{Electronics Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test.

Suppose f(x)equals 1\50 on the interval [0, 50]. a. What is the distribution of X ? b. What does the graph of f(x)look like? c. Find P ( X £ 25) d. Find P ( X ³ 25) e. Find P ( X = 25) f. Find P (0 X g. Find P ( - 3 X h. Find P (0 X

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour?

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the median waiting time for this subway?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last for more than 4,000 hours?

{Electronics Test Narrative} What is the median amount of time it takes a student to finish the test?

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours?

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability density function for this uniform distribution?