Question 1

{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 2

If X is a continuous random variable on the interval [0, 10], then P ( X > 5)= P ( X ³ 5).

Accepted Answer

A) True 
 B)False

Question 3

Suppose you have an F distribution with degrees of freedom 10, 20. 
 a. Find the mean 
 b. Find the variance. 
 c. Find the standard deviation.

Accepted Answer

The answer of Suppose you have an F distribution with...

Question 4

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.){Calculus Scores Narrative} 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...

Question 5

In the standard normal distribution, z 0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.

Accepted Answer

A) True 
 B)False

Question 6

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 7

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 8

In its standardized form, the normal distribution:

Accepted Answer

A) has a mean of 0 and a standard deviation of 1. 
B) has a mean of 1 and a variance of 0. 
C) has an area equal to 0.5. 
D) cannot be used to approximate discrete probability distributions.

Question 9

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 10

To be a legitimate probability density function, all possible values of f(x)must lie between 0 and 1 (inclusive).

Accepted Answer

A) True 
 B)False

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

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 13

To find the probability for a uniform random variable you take the ____________________ times the ____________________ of its corresponding rectangle.

Accepted Answer

The answer of To find the probability for a uniform...

Question 14

The total area under f(x)for a continuous random variable must equal ____________________.

Accepted Answer

The answer of The total area under f(x)for a continuous...

Question 15

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

Accepted Answer

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

Question 16

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. {Checking Accounts Narrative} What proportion of customers have monthly balances between $950 and $1,075?

Accepted Answer

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

Question 17

The expected value of the Student t distribution is zero.

Accepted Answer

A) True 
 B)False

Question 18

Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

Accepted Answer

A) True 
 B)False

Question 19

Which of the following has a mean and variance that depend on degrees of freedom?

Accepted Answer

A) Student t 
B) c 2 
C) F 
D) All of these choices are true.

Question 20

The probability density function f(x)for a uniform random variable X defined over the interval [2, 10] is

Accepted Answer

A) 0.20 
B) 8 
C) 4 
D) None of these choices.

Exam 7: Continuous Probability Distributions

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

If X is a continuous random variable on the interval [0, 10], then P ( X > 5)= P ( X ³ 5).

Suppose you have an F distribution with degrees of freedom 10, 20. a. Find the mean b. Find the variance. c. Find the standard deviation.

In the standard normal distribution, z _0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.

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 between one and two hours?

In its standardized form, the normal distribution:

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?

To be a legitimate probability density function, all possible values of f(x)must lie between 0 and 1 (inclusive).

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?

To find the probability for a uniform random variable you take the times the of its corresponding rectangle.

The total area under f(x)for a continuous random variable must equal ____________________.

The expected value of the Student t distribution is zero.

Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

Which of the following has a mean and variance that depend on degrees of freedom?

The probability density function f(x) for a uniform random variable X defined over the interval [2, 10] is