Question 1

The expected value, E(X), of a uniform random variable X defined over the interval $a \leq x \leq b$ , is:

Accepted Answer

A) a + b. 
B) a - b. 
C) (a + b)/2. 
D) (a - b)/2.

Question 2

Find the following probabilities: 
a. $P ( X \leq 1 )$
b. $P ( X \geq 2 )$
c. $P ( 1 \leq X \leq 2 )$
d. $P ( X = 3 )$

Accepted Answer

The answer of Find the following probabilities: 
a. \(P (...

Question 3

Given that z is a standard normal random variable, a negative value of z indicates that the standard deviation of z is negative.

Accepted Answer

A) True 
 B)False

Question 4

Given that X is a normal variable, which of the following statements is (are) true?

Accepted Answer

A) The variable X + 5 is also normally distributed. 
B) The variable X - 5 is also normally distributed. 
C) The variable 5X is also normally distributed. 
D) All of these choices are correct.

Question 5

In the normal distribution, the total area under the curve is equal to one.

Accepted Answer

A) True 
 B)False

Question 6

The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is:

Accepted Answer

A) any value between 1 and 11. 
B) 0.100. 
C) 0.091. 
D) above 11.

Question 7

Consider a binomial random variable X with n = 300 and p = 0.02. Approximate the values of the following probabilities.
a. P(X = 4).
b. P(X F1F1F1S1F1F1F10 5).
c. P(X F1F1F1S1F1F1F10 8).

Accepted Answer

The answer of Consider a binomial random variable X with...

Question 8

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

Accepted Answer

A) True 
 B)False

Question 9

Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?

Accepted Answer

A) E(X) = (a + b)/2. 
B) V(X) = $( b - a ) ^ { 2 }$ /12. 
C)  $\sigma$ = (b - a)/6. 
D)  $f ( x ) = 1 / ( b - a )$ if a F1F1F1S1?F1F1F10 x F1F1F1S1?F1F1F10 b.

Question 10

In a shopping centre, the waiting time for an elevator is found to be uniformly distributed between 1 and 5 minutes.
a. What is the probability density function for this uniform distribution?
b. What is the probability of waiting no more than 3 minutes?
c. What is the probability that the elevator arrives in the first 30 seconds?
d. What is the probability of a waiting time between 2 and 3 minutes?
e. What is the expected waiting time?

Accepted Answer

The answer of In a shopping centre, the waiting time...

Question 11

Given that Z is a standard normal random variable, the mean of Z is:

Accepted Answer

A) smaller than the median. 
B) larger than the mode. 
C) always equal to zero. 
D) always smaller than zero.

Question 12

Which of the following distributions is not symmetrical?

Accepted Answer

A) Exponential 
B) Uniform. 
C) Normal. 
D) None of these choices are correct.

Question 13

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as:

Accepted Answer

A) P(Z $\geq$ z). 
B) P(Z $\leq$ z). 
C) P(0 $\leq$ Z $\leq$ z). 
D) P(Z $\geq$ -z).

Question 14

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

Accepted Answer

A) 0.125. 
B) 0.975. 
C) 0.625. 
D) 0.500.

Question 15

The probability density function, f(x), for any continuous random variable X, represents:

Accepted Answer

A) all possible values that X will assume within some interval a F1F1F1S1F1F1F10 x F1F1F1S1F1F1F10 b. 
B) the probability that X takes on a specific value x. 
C) the area under the curve at x. 
D) the height of the function at x.

Question 16

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.1003

Accepted Answer

A) True 
 B)False

Question 17

If the random variable X is uniformly distributed over the interval 10 $\leq$ x $\leq$ 50, find the following probabilities. 
a. $P ( X \geq 30 )$
b. $P ( X \leq 25 )$
c. $P ( 18 \leq X \leq 35 )$
d. $P ( X = 40 )$

Accepted Answer

The answer of If the random variable X is uniformly...

Question 18

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

Accepted Answer

A) True 
 B)False

Question 19

Which of the following is always true for all probability density functions of continuous random variables?

Accepted Answer

A) They are symmetrical. 
B) They are bell-shaped. 
C) The area under the curve is 1.0. 
D) They have the same height.

Question 20

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X?

Accepted Answer

A) The mean of X will be greater than the standard deviation of X. 
B) The mean of X will be smaller than the standard deviation of X. 
C) The mean of X will equal the standard deviation of X. 
D) None of these choices are correct.

Exam 8: Continuous Probability Distributions

The expected value, E(X) , of a uniform random variable X defined over the interval $a \leq x \leq b$ , is:

Find the following probabilities: a. $P ( X \leq 1 )$ b. $P ( X \geq 2 )$ c. $P ( 1 \leq X \leq 2 )$ d. $P ( X = 3 )$

Given that z is a standard normal random variable, a negative value of z indicates that the standard deviation of z is negative.

Given that X is a normal variable, which of the following statements is (are) true?

In the normal distribution, the total area under the curve is equal to one.

The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is:

Consider a binomial random variable X with n = 300 and p = 0.02. Approximate the values of the following probabilities. a. P(X = 4). b. P(X  5). c. P(X  8).

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?

Given that Z is a standard normal random variable, the mean of Z is:

Which of the following distributions is not symmetrical?

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as:

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

The probability density function, f(x) , for any continuous random variable X, represents:

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.1003

If the random variable X is uniformly distributed over the interval 10 $\leq$ x $\leq$ 50, find the following probabilities. a. $P ( X \geq 30 )$ b. $P ( X \leq 25 )$ c. $P ( 18 \leq X \leq 35 )$ d. $P ( X = 40 )$

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

Which of the following is always true for all probability density functions of continuous random variables?

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X?

Exam 8: Continuous Probability Distributions

The expected value, E(X) , of a uniform random variable X defined over the interval a≤x≤ba \leq x \leq ba≤x≤b , is:

Find the following probabilities: a. P(X≤1)P ( X \leq 1 )P(X≤1) b. P(X≥2)P ( X \geq 2 )P(X≥2) c. P(1≤X≤2)P ( 1 \leq X \leq 2 )P(1≤X≤2) d. P(X=3)P ( X = 3 )P(X=3)

Given that z is a standard normal random variable, a negative value of z indicates that the standard deviation of z is negative.

Given that X is a normal variable, which of the following statements is (are) true?

In the normal distribution, the total area under the curve is equal to one.

The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is:

Consider a binomial random variable X with n = 300 and p = 0.02. Approximate the values of the following probabilities. a. P(X = 4). b. P(X  5). c. P(X  8).

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

Which of the following is not true for a random variable X that is uniformly distributed over the interval a≤x≤ba \leq x \leq ba≤x≤b ?

Given that Z is a standard normal random variable, the mean of Z is:

Which of the following distributions is not symmetrical?

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as:

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

The probability density function, f(x) , for any continuous random variable X, represents:

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.1003

If the random variable X is uniformly distributed over the interval 10 ≤\leq≤ x ≤\leq≤ 50, find the following probabilities. a. P(X≥30)P ( X \geq 30 )P(X≥30) b. P(X≤25)P ( X \leq 25 )P(X≤25) c. P(18≤X≤35)P ( 18 \leq X \leq 35 )P(18≤X≤35) d. P(X=40)P ( X = 40 )P(X=40)

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

Which of the following is always true for all probability density functions of continuous random variables?

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X?

The expected value, E(X) , of a uniform random variable X defined over the interval $a \leq x \leq b$ , is:

Find the following probabilities: a. $P ( X \leq 1 )$ b. $P ( X \geq 2 )$ c. $P ( 1 \leq X \leq 2 )$ d. $P ( X = 3 )$

Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?

If the random variable X is uniformly distributed over the interval 10 $\leq$ x $\leq$ 50, find the following probabilities. a. $P ( X \geq 30 )$ b. $P ( X \leq 25 )$ c. $P ( 18 \leq X \leq 35 )$ d. $P ( X = 40 )$