Question 1

Calculus Scores: Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.)
-What is the probability that a randomly selected student will have a score of 94 or lower?

Accepted Answer

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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.
-What is the probability density function for this uniform distribution?

Accepted Answer

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

Question 3

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-Find the probability that a student will take exactly one hour to finish the test.

Accepted Answer

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

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.
-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 has...

Question 5

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-What is the median amount of time it takes a student to finish the test?

Accepted Answer

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

Question 6

Checking Accounts: A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250.
-What proportion of customers have monthly balances more than $1,125?

Accepted Answer

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Question 7

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-What is the mean amount of time it takes a student to finish the test?

Accepted Answer

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

Question 8

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.
-What proportion of these batteries will last less than 3,600 hours?

Accepted Answer

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

Question 9

Checking Accounts: A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250.
-What proportion of customers have monthly balances less than $1,000?

Accepted Answer

The answer of Checking Accounts: A bank has determined that...

Question 10

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.
-What proportion of the dieters lost more than 12 pounds?

Accepted Answer

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

Question 11

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.
-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 has...

Question 12

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.
-If a dieter is selected at random, what is the probability that the dieter lost more than 7.5 pounds?

Accepted Answer

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Question 13

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-Find the probability that a student will take no less than 55 minutes to finish the test.

Accepted Answer

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

Question 14

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.
-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 has...

Question 15

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

Accepted Answer

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

Question 17

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.
-What proportion of the dieters gained weight?

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Calculus Scores: Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.)
-What is the probability that a randomly selected student will have a score of 80 or higher?

Accepted Answer

The answer of Calculus Scores: Scores of high school students...

Question 20

Calculus Scores: Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.)
-What is the probability that a randomly selected student will have a score between 80 and 90?

Accepted Answer

The answer of Calculus Scores: Scores of high school students...

Quiz 7: Continuous Probability Distributions

Calculus Scores: Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.) -What is the probability that a randomly selected student will have a score of 94 or lower?

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

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -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. -What proportion of these batteries will last between 3,800 and 4,100 hours?

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -What is the median amount of time it takes a student to finish the test?

Checking Accounts: A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250. -What proportion of customers have monthly balances more than $1,125?

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -What is the mean amount of time it takes a student 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. -What proportion of these batteries will last less than 3,600 hours?

Checking Accounts: A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250. -What proportion of customers have monthly balances less than $1,000?

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. -What proportion of the dieters lost more than 12 pounds?

Electronics Test: The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -Find the probability that a student will take no less than 55 minutes 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. -What proportion of these batteries will last for more than 4,000 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. -What is the probability that the subway arrives in the first minute and a half?

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

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. -What proportion of the dieters gained weight?

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

Calculus Scores: Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.) -What is the probability that a randomly selected student will have a score of 80 or higher?

Calculus Scores: Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.) -What is the probability that a randomly selected student will have a score between 80 and 90?