Question 1

If x is a random variable, and random variable y is defined as follows, y = a + bx, then  .

Accepted Answer

False

Question 2

Which of the following random variables are continuous? I). the air pressure in an automobile tire (in pounds per square inch)II). the diameter of an automobile tire (in centimeters)III). the number of miles traveled by an automobile tire
A)I only
B)I and III only
C)II and III only
D)I, II, and III
E)None of the variables is continuous.

Accepted Answer

E

Question 3

If random variables  and  are independent, then  .

Accepted Answer

True

Question 4

Determine the area under the z curve to the right of -1.82 ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Determine the area under the z curve...

Question 5

For a discrete random variable,  .

Accepted Answer

The answer of For a discrete random variable,  ....

Question 6

A random variable is continuous if the set of possible values includes an entire interval on the number line.

Accepted Answer

A continuous random variable can take on any value within a certain range, which means it includes an entire interval on the number line.

Question 7

A gasoline tank for a certain car is designed to hold 19 gallons of gas. Suppose that the random variable x = actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 19.0 gallons and standard deviation 0.2 gallon. ​
What is the probability that a randomly selected tank will hold at least 18.9 gallons?
​
A)0.19
B)0.69
C)1
D)0.31
E)0.81

Accepted Answer

The answer of A gasoline tank for a certain car...

Question 8

For random variables, x and y, if y = a + bx, then  .

Accepted Answer

The answer of For random variables, x and y, if...

Question 9

Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year's graduates:  Consider the variable x = amount of donation for a person selected at random from the population of last year's graduates of this university.What is  ?
A)0.10
B)0.50
C)0.55
D)0.75
E)0.90

Accepted Answer

The answer of Suppose that fund-raisers at a university call...

Question 10

For a discrete random variable x,  .

Accepted Answer

The answer of For a discrete random variable x, ...

Question 11

Suppose x is a continuous random variable with the probability distribution shouwn below.  What probability is represented by the shaded area?
A) 
B) 
C) 
D) 
E)none of these

Accepted Answer

The answer of Suppose x is a continuous random variable...

Question 12

For a continuous random variable x, the height of the density curve over an interval a to b represents the probability that x is between a and b.

Accepted Answer

The area under the density curve over an interval a to b represents the probability that x is between a and b, not the height of the curve.

Question 13

Which of the following random variables are discrete? I). the volume of a balloon in liters
II)) the number of helium atoms in a balloon
II)) the number of balloons at a birthday party
A)I only
B)II only
C)III only
D)II and III only
E)I, II, and III

Accepted Answer

II and III are discrete because they can only take on integer values (you can't have a fraction of an atom or balloon), while volume can vary continuously.

Question 14

A random variable is discrete if the value of the random variable depends upon the outcome of a chance experiment.

Accepted Answer

A random variable is considered discrete if it can take on a countable number of distinct values, not necessarily because its value depends on the outcome of a chance experiment. Both discrete and continuous random variables depend on the outcomes of chance experiments, but they differ in the type of values they can take.

Question 15

For every random variable,  .

Accepted Answer

The answer of For every random variable,  ....

Question 16

The standard normal distribution has a mean of 1 and standard deviation of 0.

Accepted Answer

The standard normal distribution has a mean of 0 and standard deviation of 1.

Question 17

The distribution of all values of a random variable is called a normal distribution.

Accepted Answer

The distribution of all values of a normal random variable is called a normal distribution.

Question 18

A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for the following random variable. x= number of slips marked "1" ​
A) 0,1
B) 0,1,2
C)2
D)0
E)1

Accepted Answer

Since there is only one slip marked "1," when two slips are selected without replacement, the possible outcomes for the number of slips marked "1" are either getting the slip marked "1" (which can happen once) or not getting it at all. Therefore, the possible values for x are 0 and 1.

Question 19

A normal probability plot suggests that a normal probability model is plausible if there is no obvious pattern in the scatter of points.

Accepted Answer

The answer of A normal probability plot suggests that a...

Question 20

A chemical supply company currently has in stock 100 pounds of a certain chemical, which it sells to customers in 5-pound lots. Let  the number of lots ordered by a randomly chosen customer. The probability distribution of x is as follows:  Calculate the mean value of x.
A)2.2
B)2.5
C)2.7
D)3.3
E)3.7

Accepted Answer

The answer of A chemical supply company currently has in...

Quiz 6: Random Variables and Probability Distributions

If x is a random variable, and random variable y is defined as follows, y = a + bx, then .

Which of the following random variables are continuous? I) . the air pressure in an automobile tire (in pounds per square inch) II) . the diameter of an automobile tire (in centimeters) III) . the number of miles traveled by an automobile tire

If random variables and are independent, then .

Determine the area under the z curve to the right of -1.82

For a discrete random variable, .

A random variable is continuous if the set of possible values includes an entire interval on the number line.

For random variables, x and y, if y = a + bx, then .

For a discrete random variable x, .

Suppose x is a continuous random variable with the probability distribution shouwn below. What probability is represented by the shaded area?

For a continuous random variable x, the height of the density curve over an interval a to b represents the probability that x is between a and b.

Which of the following random variables are discrete? I) . the volume of a balloon in liters II) ) the number of helium atoms in a balloon II) ) the number of balloons at a birthday party

A random variable is discrete if the value of the random variable depends upon the outcome of a chance experiment.

For every random variable, .

The standard normal distribution has a mean of 1 and standard deviation of 0.

The distribution of all values of a random variable is called a normal distribution.

A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for the following random variable. x= number of slips marked "1"

A normal probability plot suggests that a normal probability model is plausible if there is no obvious pattern in the scatter of points.

A chemical supply company currently has in stock 100 pounds of a certain chemical, which it sells to customers in 5-pound lots. Let the number of lots ordered by a randomly chosen customer. The probability distribution of x is as follows: Calculate the mean value of x.

Quiz 6: Random Variables and Probability Distributions

If x is a random variable, and random variable y is defined as follows, y = a + bx, then .

Which of the following random variables are continuous? I) . the air pressure in an automobile tire (in pounds per square inch) II) . the diameter of an automobile tire (in centimeters) III) . the number of miles traveled by an automobile tire

If random variables and are independent, then .

Determine the area under the z curve to the right of -1.82 ​

For a discrete random variable, .

A random variable is continuous if the set of possible values includes an entire interval on the number line.

For random variables, x and y, if y = a + bx, then .

For a discrete random variable x, .

Suppose x is a continuous random variable with the probability distribution shouwn below. What probability is represented by the shaded area?

For a continuous random variable x, the height of the density curve over an interval a to b represents the probability that x is between a and b.

Which of the following random variables are discrete? I) . the volume of a balloon in liters II) ) the number of helium atoms in a balloon II) ) the number of balloons at a birthday party

A random variable is discrete if the value of the random variable depends upon the outcome of a chance experiment.

For every random variable, .

The standard normal distribution has a mean of 1 and standard deviation of 0.

The distribution of all values of a random variable is called a normal distribution.

A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for the following random variable. x= number of slips marked "1" ​

A normal probability plot suggests that a normal probability model is plausible if there is no obvious pattern in the scatter of points.

A chemical supply company currently has in stock 100 pounds of a certain chemical, which it sells to customers in 5-pound lots. Let the number of lots ordered by a randomly chosen customer. The probability distribution of x is as follows: Calculate the mean value of x.

Determine the area under the z curve to the right of -1.82

A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for the following random variable. x= number of slips marked "1"