Question 1

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. {Montana Highways Narrative} What is the distribution of X ?

Accepted Answer

The answer of Montana Highways A recent survey in Montana...

Question 2

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below.  
 {Shopping Outlet Narrative} What did you notice about the mean, variance, and standard deviation of Y = 2 X + 1 in terms of the mean, variance, and standard deviation of X ?

Accepted Answer

The answer of Shopping Outlet A shopping outlet estimates the...

Question 3

911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center. {911 Phone Calls Narrative} Find the probability of receiving two calls in a five-minute interval of time.

Accepted Answer

The answer of 911 Phone Calls 911 phone calls arrive...

Question 4

Stress Consider a binomial random variable X with n = 5 and p = 0 . 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed. {Stress Narrative} Find the expected number of times a student may feel stressed during the final exam week.

Accepted Answer

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

Question 5

The mean of a binomial distribution is equal to ____________________.

Accepted Answer

The answer of The mean of a binomial distribution is...

Question 6

Retries The following table contains the probability distribution for X = the number of retries necessary to successfully transmit a 1024K data package through a double satellite media.  {Retries Narrative} What is the probability of no retries?

Accepted Answer

The answer of Retries The following table contains the probability...

Question 7

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. {Montana Highways Narrative} Find the standard deviation of number of vehicles that are traveling on Montana highways and exceeding the speed limit.

Accepted Answer

The answer of Montana Highways A recent survey in Montana...

Question 8

If X has a binomial distribution with n = 4 and p = 0.3, find the probability that X is at least one.

Accepted Answer

The answer of If X has a binomial distribution with...

Question 9

A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities, is called a(n):

Accepted Answer

A) discrete probability distribution. 
B) discrete random variable. 
C) expected value of a discrete random variable. 
D) None of these choices.

Question 10

In the notation below, X is the random variable, E and V refer to the expected value and variance, respectively. Which of the following is false?

Accepted Answer

A) E (3 X )= 3 E ( X ) 
B) V (2)= 0 
C) E ( X + 1)= E ( X )+ 1 
D) All of these choices are true.

Question 11

A Poisson random variable is a(n)____________________ random variable.

Accepted Answer

The answer of A Poisson random variable is a(n)____________________ random...

Question 12

Let X be a Poisson random variable with m = 6. Use the table of Poisson probabilities to calculate: 
 a. P ( X £ 8)
 b. P ( X = 8)
 c. P ( X ³ 5)
 d. P (6 £ X £ 10)

Accepted Answer

The answer of Let X be a Poisson random variable...

Question 13

Classified Department Phone Calls A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another. {Classified Department Phone Calls Narrative} Find the probability that the department will receive seven calls between 2 and 3 P.M. on a particular afternoon.

Accepted Answer

The answer of Classified Department Phone Calls A classified department...

Question 14

The Poisson random variable is a discrete random variable with infinitely many possible values.

Accepted Answer

A) True 
 B)False

Question 15

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. 
 x 0 1 2 3 4 
 p ( x )0.05 0.35 0.25 0.20 0.15 
 {Shopping Outlet Narrative} Suppose Y = 2 X + 1 for each value of X . What is the probability distribution of Y ?

Accepted Answer

The answer of Shopping Outlet A shopping outlet estimates the...

Question 16

Blackjack The probability distribution of a random variable X is shown below, where X represents the amount of money (in $1,000s)gained or lost in a particular game of Blackjack.  {Blackjack Narrative} Find the following values, and indicate their units. 
 a. E ( X )
 b. V ( X )
 c. Standard deviation of X

Accepted Answer

The answer of Blackjack The probability distribution of a random...

Question 17

Given a Poisson random variable X , where the average number of successes occurring in a specified interval is 1.8, then P ( X = 0)is:

Accepted Answer

A) 1.8 
B) 1.3416 
C) 0.1653 
D) 6.05

Question 18

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Accepted Answer

A) True 
 B)False

Question 19

Number of Motorcycles The probability distribution of a discrete random variable X is shown below, where X represents the number of motorcycles owned by a family. 
  {Number of Motorcycles Narrative} Apply the laws of expected value and variance to find the following: 
 a. V( 3 X)
 b. V (3 X - 2)
 c. V( 3 )
 d. V( 3 X)- 2

Accepted Answer

The answer of Number of Motorcycles The probability distribution of...

Question 20

A remedial program evenly enrolls tradition and non-traditional students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new on-line class, what is the probability that all 4 students selected are traditional students?

Accepted Answer

The answer of A remedial program evenly enrolls tradition and...

Exam 6: Random Variables and Discrete Probability Distributions

911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center. {911 Phone Calls Narrative} Find the probability of receiving two calls in a five-minute interval of time.

Stress Consider a binomial random variable X with n = 5 and p = 0 . 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed. {Stress Narrative} Find the expected number of times a student may feel stressed during the final exam week.

The mean of a binomial distribution is equal to ____________________.

Retries The following table contains the probability distribution for X = the number of retries necessary to successfully transmit a 1024K data package through a double satellite media. {Retries Narrative} What is the probability of no retries?

If X has a binomial distribution with n = 4 and p = 0.3, find the probability that X is at least one.

A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities, is called a(n) :

In the notation below, X is the random variable, E and V refer to the expected value and variance, respectively. Which of the following is false?

A Poisson random variable is a(n)____________________ random variable.

Let X be a Poisson random variable with m = 6. Use the table of Poisson probabilities to calculate: a. P ( X £ 8) b. P ( X = 8) c. P ( X ³ 5) d. P (6 £ X £ 10)

The Poisson random variable is a discrete random variable with infinitely many possible values.

Given a Poisson random variable X , where the average number of successes occurring in a specified interval is 1.8, then P ( X = 0) is:

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

A remedial program evenly enrolls tradition and non-traditional students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new on-line class, what is the probability that all 4 students selected are traditional students?