PSYC 7302 Module 4

A ____ variable assigns a unique numerical value to each outcome of a random experiment.

random

____________ random variables have an infinite continuum of possible values

Continuous

The number of times that a hiker walks over 8 miles each day is what type of data random variable? A. Discrete B. Continuous

A. Discrete

Consider the following statements about a particular University and it's student population. Which of these variables in continuous? Select all that apply. A. The average income of a student's family B. The number of classes a student has taken since enrollment. C. The number of classes a student is taking in the current semester. D. The University's ranking among other colleges in the state.

A. The average income of a student's family B. The number of classes a student has taken since enrollment.

Skewness describes information about the "peakedness" of the distribution. A True B False

False

The number of people in a car that crosses a certain bridge is represented by the random variable X, which has a mean value μX=2.7, and a variance σ2X=1.2. The toll on the bridge is $3.00 per car plus $0.50 per person in the car. What is the variance of the total amount of money that is collected from a car that crosses the bridge? ________ Report your answer to two decimal places. Do NOT include a dollar sign ($) when reporting your answer.

.30

The number of people entering a state park is a random variable X with a mean of 3 and a variance of 2. The admission to the park is $6 per car plus an additional $1.50 per person in the car. What is the mean of the total amount of money collected for a car entering the park? ________ Report your answer to two decimal places. Do NOT include a dollar sign ($) when reporting your answer.

10.50

The number of people in a car that crosses a certain bridge is represented by the random variable X, which has a mean value μX=2.7, and a variance σ2X=1.2. The toll on the bridge is $3.00 per car plus $0.50 per person in the car. What is the mean of the total amount of money that is collected from a car that crosses the bridge? ____________ Report your answer to two decimal places. Do NOT include a dollar sign ($) when reporting your answer.

4.35

The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below. 0=.50 1=.25 2=.15 3=.06 4=.03 5=.01 What is the probability that in a given shift there will be at most 2 defects? A. 0.90 B. 0.75 C. 0.40 D. 0.10 E. 1.00

A. 0.90

A building has two elevators, an express elevator and a standard elevator. Let X be the number of passengers using the express elevator every hour, and let Y be the number of passengers using the standard elevator every hour. Assuming that μ X = 55 and μ Y = 32, what is the mean of Z, the total number of passengers using the elevators each hour? A. 23 B. 32 C. 55 D. 87

D. 87

_______ random variables exist if possible values are a distinct list.

Discrete

The _____ of a random variable is notated as μX.

mean

The _____ of a random variable is notated as σ2x.

variance

To find descriptive statistics for categorical variables, you should use _______. This will tell you how many people gave each response. A Percentages B Frequencies C Descriptive D Histograms

B Frequencies

The number of people per car admitted to a drive in movie theater is a random variable X having a mean value of 4.9 and a variance of 1.4. The cost of a movie ticket is $8 per car plus $2 per person in the car. An expression for the amount of money that is collected from a car that crosses the bridge is:

8+2X

Which of the following variables is discrete? A. Shoe size B. Waist measurement C. Foot length D. Dress size

A. Shoe size D. Dress size

The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: 0=.20 1=.30 2=.20 3=.15 4=.10 5=.05 By the third day of a particular week, 2 accidents have already occurred in the intersection. What is the probability that there will be less than a total of 4 accidents during that week? A. 1.00 B. 0.90 C. 0.85 D. 0.70 E. 0.50

D. 0.70

A parking garage has two entrances. Let X be the number of cars that enter the garage through door A in an hour, and Y be the number of cars that enter through door B in an hour.Assuming that μX=15 and μY=25, what is the mean of Z, the total number of cars that enter the garage in an hour? A. 10 B. 15 C. 25 D. 40

D. 40

___________ random variables have a countable number of outcomes

Discrete

The Coff-E-Cup beverage company has opened two franchises in town. They put one location in the center of town and one at the west end of town. Let X be the number of customers that enter the center of town location in an hour, and Y be the number of customers that enter the location at the west end of town in an hour. Assuming that μX=65 with σX=4.3 and μY=45 with σY=3.2, what is the mean of Z, the total number of customers that enter these locations in an hour? A. 20 B. 55 C. 65 D. 45 E. 110

E. 110

The number of people entering a state park is a random variable X with a mean of 3 and a variance of 2. The admission to the park is $6 per car plus an additional $2 per person in the car. Which of the following is an expression for the total amount of money collected for a car entering the park? A. 6X+2 B. 2X+6 C. 3X+6 D. 3X+2

B. 2X+6

Joe went to watch the Quakes play baseball at Epicenter stadium in Rancho Cucamonga. While he enjoyed the game, he also purchased some food. Consider whether some of the things he saw or did at the game that involve discrete or continuous variables. Which of the following is a true statement? A. The batting average of Joe's favorite player is a continuous variable. B. The number of hot dogs that Joe bought is a discrete variable. C. The number of strikeouts in the game is a continuous variable. D. The Quakes standings in the league is a discrete variable.

A. The batting average of Joe's favorite player is a continuous variable. B. The number of hot dogs that Joe bought is a discrete variable. D. The Quakes standings in the league is a discrete variable.

Suppose Blue Cab Company charges $2.85 a ride up to 0.1 miles and $0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the standard deviation of the fare passengers pay? A. $0.42 B. $4.20 C. $9.00

B. $4.20

The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: 0=.20 1=.30 2=.20 3=.15 4=.10 5=.05 What is the probability that in a given week there will be at most 3 accidents? A. 0.70 B. 0.85 C. 0.35 D. 0.15 E. 1.00

B. 0.85

The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: 0=.20 1=.30 2=.20 3=.15 4=.10 5=.05 On average, how many accidents are there in the intersection in a week? A. 5.3 B. 2.5 C. 1.8 D. 0.30 E. 0.1667

C. 1.8

Which of these is NOT continuous? A. the weight of a car B. the number of students in a classroom C. a person's height D. the ounces of tears cried by a student in a statistics course

B. the number of students in a classroom

Safari Adventure Theme Park is a selfguided theme park in which people drive through a park filled with African wildlife. They are given a map and a written guide to the wildlife of the park. They charge $20.00 per car plus $2.00 per person in the car. The number of people per car can be represented by the random variable X which has a mean value μX=3.2, and a variance σ2x=1.4.What is the mean of the total amount of money per car that is collected entering the park? A. $6.40 B. $66.00 C. $26.40 D. $22.00

C. $26.40

The random variable X, representing the number of items sold in a week, has the following probability distribution: 0=0.10 1=0.20 2=0.40 3=0.15 4=0.05 5=0.05 6=0.05 By the fourth day of a particular week, 3 items have already sold. What is the probability that there will be less than a total of 5 items sold during that week? A. 1.00 B. 0.95 C. 0.90 D. 0.85 E. 0.67

E. 0.67

Safari Adventure Theme Park is a selfguided theme park in which people drive through a park filled with African wildlife. They are given a map and a written guide to the wildlife of the park. They charge $20.00 per car plus $2.00 per person in the car. The number of people per car can be represented by the random variable X which has a mean value μX=3.2, and a variance σ2x=1.4.What is the variance of the total amount of money per car that is collected entering the park? A. $5.60 B. $2.80 C. $26.40 D. $4.00

A. $5.60

According the the Pew Research Center, the probability of a randomly selected person living in the United States identifying with a particular religious affiliation—Protestant Christian; Catholic Christian, Other Christian, Non-Christian (including Jewish, Muslim, Buddhist, Hindu and other religions); and Unaffiliated (the so-called "nones")—is shown in the following chart. Protestant Christian=.466 Catholic Christian=.208 Other Christian=.033 Non-Christian=.06 Unaffiliated "none"=.233 Assuming this data is accurate and stable, what is the probability that a randomly selected person living in the United States would not identify as Christian? A. 0.293 B. 0.06 C. 0.707

A. 0.293

Salary of an employee at a large company is a random variable X with a mean of $50,000 and a variance of $2,700. The CEO of the company decides to give every employee a 2% raise and a $500 bonus. Which of the following is an expression for an employee's new salary? A. 500 + 1.02X B. 500 + 0.02X C. 1.02 + 500X D. 500 + 1.20X

A. 500 + 1.02X

Consider the following statements about a particular traditional class of statistics students at State U related to discrete and continuous variables. Which of the following is a true statement? A. The number of students in the class is a discrete variable. B. The average age of the students in the class is a continuous variable. C. The room number of the class is a continuous variable variable. D. The average weight of the students is a discrete variable. E. A student's GPA is a continuous variable.

A. The number of students in the class is a discrete variable. B. The average age of the students in the class is a continuous variable. E. A student's GPA is a continuous variable.

The random variable X, representing the number of items sold in a week, has the following probability distribution: 0=0.10 1=0.20 2=0.40 3=0.15 4=0.05 5=0.05 6=0.05 What is the probability that in a given week there will be at most 4 items sold? A. 0.85 B. 0.90 C. 0.60 D. 0.10 E. 1.00

B. 0.90

Daily rainfall is an example of what type of data random variable? A. Discrete B. Continuous

B. Continuous

Which of the following is a characteristic of a discrete random variable? A. It is something you measure. B. It is something you count. C. It is something you both measure and count.

B. It is something you count.

Suppose Blue Cab Company charges $2.85 a ride up to 0.1 miles and $0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the mean of the fare passengers pay? A. Mean $4.14 B. Mean $18.45 C. Mean $18.75

B. Mean $18.45

According the the Pew Research Center, the probability of a randomly selected person living in the United States identifying with a particular religious affiliation—Protestant Christian; Catholic Christian, Other Christian, Non-Christian (including Jewish, Muslim, Buddhist, Hindu and other religions); and Unaffiliated (the so-called "nones")—is shown in the following chart. Protestant Christian=.466 Catholic Christian=.208 Other Christian=.033 Non-Christian=.06 Unaffiliated "none"=.233 Assuming this data is accurate and stable, what is the probability that a randomly selected Christian living in the United States would identify as Catholic? A. 0.208 B. 0.659 C. 0.294 D. 0.707

C. 0.294

The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below. 0=.50 1=.25 2=.15 3=.06 4=.03 5=.01 After 2 hours of a particular shift, 2 defects have already been detected. What is the probability that there will be less than a total of 4 defects detected during the entire shift? A. 1.00 B. 0.96 C. 0.84 D. 0.25

C. 0.84

The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below. 0=.50 1=.25 2=.15 3=.06 4=.03 5=.01 On average, how many defects are found during an 8-hour shift? A. 5.3 B. 2.5 C. 0.9 D. 0.50 E. 0.1667

C. 0.9

The random variable X, representing the number of items sold in a week, has the following probability distribution: 0=0.10 1=0.20 2=0.40 3=0.15 4=0.05 5=0.05 6=0.05 On average, how many items are sold in a week? A. 6.3 B. 3.0 C. 2.2 D. 2.0 E. 0.1428

C. 2.2

A national park has 2 entrance gates, one at the north end and a second gate at the south end of the park. Let X be the number of cars entering the North gate per hour and let Y be the number of cars entering the South gate per hour. Assume that X is random variable with mean μ x = 23 and standard deviation σ x = 3. Assume Y is a random variable with mean μ y = 18 and standard deviation σ y = 4. Assume that the two gates operate independently. What is the standard deviation of Z, the total number of cars entering the park each hour? A. √7 B. 4 C. 5 D. 7

C. 5

The Coff-E-Cup beverage company has opened two franchises in town. They put one location in the center of town and one at the west end of town. Let X be the number of customers that enter the center of town location in an hour, and Y be the number of customers that enter the location at the west end of town in an hour. Assuming that μX=65 with σX=4.3 and μY=45 with σY=3.2, what is the standard deviation of Z, the total number of customers that enter these locations in an hour? A. 28.73 B. 7.50 C. 5.36 D. 3.75

C. 5.36

The number of computer monitors manufactured per day by CompScreens Inc. is a random variable X, with a mean μ x = 120 and a variance of σ 2 x = 36. The cost of manufacturing the monitors is $500 base cost plus $15 per monitor. What is the variance of the total cost per day for CompScreens Inc. to manufacture computer monitors? A. 540 B. 1040 C. 8100 D. 8600

C. 8100

Which of the following is a discrete data random variable? A. A person's height each birthday B. The volume of water in a swimming pool each day C. Cars finished in a factory each day D. A person's weight on each year

C. Cars finished in a factory each day

To find descriptive statistics for continuous variables, you should use ______. This will give you information about the mean, median and standard deviation of your data. A. Percentages B. Frequencies C. Descriptives D. Histograms

C. Descriptives

Consider the following statements about a particular University and it's student population. Which of these variables is discrete? Select all that apply. A. The average income of a student's family B. The number of classes a student has taken since enrollment. C. The number of classes a student is taking in the current semester. D. The University's ranking among other colleges in the state.

C. The number of classes a student is taking in the current semester. D. The University's ranking among other colleges in the state.

All probability distributions are characterized by _________ and a ________.

an expected value (mean) variance (standard deviation squared)

The probability _____ of a random variable is the list of all possible values and probabilities.

distribution