Probability B

Probability Distributions: Continuous Probability Distributions

Multiple Choice Questions

Question 1: Probability Density Function (PDF)

• Question: For a continuous random variable $x$, the probability density function $f(x)$ represents:

  • a. the probability at a given value of $x$

  • b. the area under the curve at $x$

  • c. the area under the curve to the right of $x$

  • d. the height of the function at $x$

• Answer: d. the height of the function at $x$

Question 2: Uniform Probability Distribution

• Question: The uniform probability distribution is used with:

  • a. a continuous random variable

  • b. a discrete random variable

  • c. a normally distributed random variable

  • d. any random variable, as long as it is not nominal

• Answer: a. a continuous random variable

Question 3: Probability of a Specific Value

• Question: For any continuous random variable, the probability that the random variable takes on exactly a specific value is:

  • a. 1.00

  • b. 0.50

  • c. any value between 0 to 1

  • d. almost zero

• Answer: d. almost zero

Question 4: Area to the Left of the Mean for Standard Normal Distribution

• Question: For the standard normal probability distribution, the area to the left of the mean is:

  • a. -0.5

  • b. 0.5

  • c. any value between 0 to 1

  • d. 1

• Answer: b. 0.5

Question 5: Characteristics of Normal Probability Distribution

• Question: Which of the following is not a characteristic of the normal probability distribution?

  • a. The mean, median, and the mode are equal

  • b. The mean of the distribution can be negative, zero, or positive

  • c. The distribution is symmetrical

  • d. The standard deviation must be 1

• Answer: d. The standard deviation must be 1

Question 6: Range of Values of $Z$ in Standard Normal Distribution

• Question: In a standard normal distribution, the range of values of $z$ is from:

  • a. minus infinity to infinity

  • b. -1 to 1

  • c. 0 to 1

  • d. -3.09 to 3.09

• Answer: a. minus infinity to infinity

Question 7: Uniform Probability Density Function Height

• Question: For a uniform probability density function:

  • a. the height of the function cannot be larger than one

  • b. the height of the function is the same for each value of $x$

  • c. the height of the function is different for various values of $x$

  • d. the height of the function decreases as $x$ increases

• Answer: b. the height of the function is the same for each value of $x$

Question 8: Probability Density Function for Uniform Distribution

• Question: The probability density function for a uniform distribution ranging between 2 and 6 is:

  • a. 4

  • b. undefined

  • c. any positive value

  • d. 0.25

• Answer: d. 0.25

Question 9: Probability in Uniform Distribution

• Question: A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is:

  • a. different for each interval

  • b. the same for each interval

  • c. at least one

  • d. None of these alternatives is correct

• Answer: b. the same for each interval

Question 10: Function Defining the Probability Distribution

• Question: The function that defines the probability distribution of a continuous random variable is:

  • a. normal function

  • b. uniform function

  • c. either normal or uniform depending on the situation

  • d. probability density function

• Answer: d. probability density function

Question 11: Approximating Discrete Probability Distribution

• Question: When a continuous probability distribution is used to approximate a discrete probability distribution:

  • a. a value of 0.5 is added and/or subtracted from the area

  • b. a value of 0.5 is added and/or subtracted from the value of $x$

  • c. a value of 0.5 is added to the area

  • d. a value of 0.5 is subtracted from the area

• Answer: b. a value of 0.5 is added and/or subtracted from the value of $x$

Question 12: Exponential Probability Distribution Description

• Question: A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is:

  • a. normal probability distribution

  • b. uniform probability distribution

  • c. exponential probability distribution

  • d. Poisson probability distribution

• Answer: c. exponential probability distribution

Question 13: Exponential Distribution Application

• Question: The exponential probability distribution is used with:

  • a. a discrete random variable

  • b. a continuous random variable

  • c. any probability distribution with an exponential term

  • d. an approximation of the binomial probability distribution

• Answer: b. a continuous random variable

Question 14: Probability in a Binomial Experiment

• Question: Consider a binomial probability experiment with $n = 3$ and $p = 0.1$. Then, the probability of $x = 0$ is:

  • a. 0.0000

  • b. 0.0001

  • c. 0.001

  • d. 0.729

• Answer: d. 0.729

Question 15: Impact of Standard Deviation on Normal Curve

• Question: Larger values of the standard deviation result in a normal curve that is:

  • a. shifted to the right

  • b. shifted to the left

  • c. narrower and more peaked

  • d. wider and flatter

• Answer: d. wider and flatter

Question 16: Characteristics of Normal Distribution

• Question: Which of the following is not a characteristic of the normal probability distribution?

  • a. symmetry

  • b. The total area under the curve is always equal to 1.

  • c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

  • d. The mean is equal to the median, which is also equal to the mode.

• Answer: c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

Question 17: Understanding Negative $Z$ Values

• Question: For a normal distribution, a negative value of $z$ indicates:

  • a. a mistake has been made in computations, because $z$ is always positive

  • b. the area corresponding to the $z$ is negative

  • c. the $z$ is to the left of the mean

  • d. the $z$ is to the right of the mean

• Answer: c. the $z$ is to the left of the mean

Question 18: Mean of Standard Normal Distribution

• Question: The mean of a standard normal probability distribution is:

  • a. always equal to zero

  • b. can be any value as long as it is positive

  • c. can be any value

  • d. is always greater than zero

• Answer: a. always equal to zero

Question 19: Standard Deviation of Standard Normal Distribution

• Question: The standard deviation of a standard normal distribution is:

  • a. always equal to zero

  • b. always equal to one

  • c. can be any positive value

  • d. can be any value

• Answer: b. always equal to one

Question 20: Nature of Normal Probability Distribution

• Question: A normal probability distribution:

  • a. is a continuous probability distribution

  • b. is a discrete probability distribution

  • c. can be either continuous or discrete

  • d. must have a standard deviation of 1

• Answer: a. is a continuous probability distribution

Question 21: Values of Continuous Random Variables

• Question: A continuous random variable may assume:

  • a. all values in an interval or collection of intervals

  • b. only integer values in an interval or collection of intervals

  • c. only fractional values in an interval or collection of intervals

  • d. all the positive integer values in an interval

• Answer: a. all values in an interval or collection of intervals

Question 22: PDF of Uniformly Distributed Continuous Random Variable

• Question: A continuous random variable is uniformly distributed between $a$ and $b$. The probability density function between $a$ and $b$ is:

  • a. zero

  • b. (a - b)

  • c. (b - a)

  • d. $rac{1}{b - a}$

• Answer: d. $rac{1}{b - a}$

Question 23: Mean of Normal Distribution

• Question: If the mean of a normal distribution is negative:

  • a. the standard deviation must also be negative

  • b. the variance must also be negative

  • c. a mistake has been made in the computations, because the mean of a normal distribution cannot be negative

  • d. None of these alternatives is correct

• Answer: d. None of these alternatives is correct

Question 24: Probability for Standard Normal Distribution

• Question: For a standard normal distribution, the probability of $z \leq 0$ is:

  • a. zero

  • b. -0.5

  • c. 0.5

  • d. one

• Answer: c. 0.5

Question 25: Highest Point of Normal Curve

• Question: The highest point of a normal curve occurs at:

  • a. one standard deviation to the right of the mean

  • b. two standard deviations to the right of the mean

  • c. approximately three standard deviations to the right of the mean

  • d. the mean

• Answer: d. the mean

Question 26: Probability for Uniformly Distributed Variable

• Question: The random variable $x$ is known to be uniformly distributed between 70 and 90. The probability of $x$ having a value between 80 to 95 is:

  • a. 0.75

  • b. 0.5

  • c. 0.05

  • d. 1

• Answer: b. 0.5

Question 27: Finding Probability with Standard Normal Variable

• Question: $Z$ is a standard normal random variable. The $P(-1.96 \leq Z \leq -1.4)$ equals:

  • a. 0.8942

  • b. 0.0558

  • c. 0.475

  • d. 0.4192

• Answer: b. 0.0558

Question 28: Exhibit 1 - Assembly Time

• Exhibit 1: The assembly time for a product is uniformly distributed between 6 to 10 minutes.

• Question: The probability density function has what value in the interval between 6 and 10?

  • a. 0.25

  • b. 4.00

  • c. 5.00

  • d. zero

• Answer: a. 0.25

Question 29: Probability of Assembling Between 7-9 Minutes

• Question: The probability of assembling the product between 7 to 9 minutes is:

  • a. zero

  • b. 0.50

  • c. 0.20

  • d. 1

• Answer: b. 0.50

Question 30: Probability of Assembling in Less Than 6 Minutes

• Question: The probability of assembling the product in less than 6 minutes is:

  • a. zero

  • b. 0.50

  • c. 0.15

  • d. 1

• Answer: a. zero

Question 31: Probability of Assembling in 7 Minutes or More

• Question: The probability of assembling the product in 7 minutes or more is:

  • a. 0.25

  • b. 0.75

  • c. zero

  • d. 1

• Answer: b. 0.75

Question 32: Expected Assembly Time

• Question: The expected assembly time (in minutes) is:

  • a. 16

  • b. 2

  • c. 8

  • d. 4

• Answer: c. 8

Question 33: Standard Deviation of Assembly Time

• Question: The standard deviation of assembly time (in minutes) is approximately:

  • a. 1.3333

  • b. 1.1547

  • c. 0.1111

  • d. 0.5773

• Answer: b. 1.1547

Question 34: Definition of Standard Normal Distribution

• Question: A standard normal distribution is a normal distribution:

  • a. with a mean of 1 and a standard deviation of 0

  • b. with a mean of 0 and a standard deviation of 1

  • c. with any mean and a standard deviation of 1

  • d. with any mean and any standard deviation

• Answer: b. with a mean of 0 and a standard deviation of 1

Question 35: Probabilities for Standard Normal Random Variables

• Question: $Z$ is a standard normal random variable. The $P(1.20 \leq Z \leq 1.85)$ equals:

  • a. 0.4678

  • b. 0.3849

  • c. 0.8527

  • d. 0.0829

• Answer: d. 0.0829

Question 36: Probabilities with Standard Normal Distribution

• Question: $Z$ is a standard normal random variable. The $P(-1.20 \leq Z \leq 1.50)$ equals:

  • a. 0.0483

  • b. 0.3849

  • c. 0.4332

  • d. 0.8181

• Answer: d. 0.8181

Question 37: Exhibit 2 - Weight of Football Players

• Exhibit 2: The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

• Question: The probability of a player weighing more than 241.25 pounds is:

  • a. 0.4505

  • b. 0.0495

  • c. 0.9505

  • d. 0.9010

• Answer: b. 0.0495

Question 38: Probability of a Player Weighing Less than 250 Pounds

• Question: The probability of a player weighing less than 250 pounds is:

  • a. 0.4772

  • b. 0.9772

  • c. 0.0528

  • d. 0.5000

• Answer: b. 0.9772

Question 39: Percent of Players Weighing Between 180 and 220 Pounds

• Question: What percent of players weigh between 180 and 220 pounds?

  • a. 28.81%

  • b. 0.5762%

  • c. 0.281%

  • d. 57.62%

• Answer: d. 57.62%

Question 40: Minimum Weight of the Middle 95% of Players

• Question: What is the minimum weight of the middle 95% of the players?

  • a. 196

  • b. 151

  • c. 249

  • d. 190

• Answer: b. 151

Question 41: Probability of $-2.51 \leq Z \leq -1.53$

• Question: Given that $Z$ is a standard normal random variable, what is the probability that $-2.51 \leq Z \leq -1.53$?

  • a. 0.4950

  • b. 0.4370

  • c. 0.0570

  • d. 0.9310

• Answer: c. 0.0570

Question 42: Probability that $Z \geq -2.12$

• Question: Given that $Z$ is a standard normal random variable, what is the probability that $Z \geq -2.12$?

  • a. 0.4830

  • b. 0.9830

  • c. 0.017

  • d. 0.966

• Answer: b. 0.9830

Question 43: Probability that $-2.08 \leq Z \leq 1.46$

• Question: Given that $Z$ is a standard normal random variable, what is the probability that $-2.08 \leq Z \leq 1.46$?

  • a. 0.9091

  • b. 0.4812

  • c. 0.4279

  • d. 0.0533

• Answer: a. 0.9091

Question 44: Exhibit 3 - Uniform Distribution

• Exhibit 3: Consider the continuous random variable $X$, which has a uniform distribution over the interval from 20 to 28.

• Question: The probability density function has what value in the interval between 20 and 28?

  • a. 0

  • b. 0.050

  • c. 0.125

  • d. 1.000

• Answer: c. 0.125

Question 45: Probability of $X$ between 21 and 25

• Question: The probability that $X$ will take on a value between 21 and 25 is:

  • a. 0.125

  • b. 0.250

  • c. 0.500

  • d. 1.000

• Answer: c. 0.500

Question 46: Probability of $X$ at least 26

• Question: The probability that $X$ will take on a value of at least 26 is:

  • a. 0.000

  • b. 0.125

  • c. 0.250

  • d. 1.000

• Answer: c. 0.250

Question 47: Mean of $X$

• Question: The mean of $X$ is:

  • a. 0.000

  • b. 0.125

  • c. 23

  • d. 24

• Answer: d. 24

Question 48: Variance of $X$

• Question: The variance of $X$ is approximately:

  • a. 2.309

  • b. 5.333

  • c. 32

  • d. 0.667

• Answer: b. 5.333

Question 49: Probability for P(1.41 < Z < 2.85)

• Question: $Z$ is a standard normal random variable. The P(1.41 < Z < 2.85) equals:

  • a. 0.4978

  • b. 0.4207

  • c. 0.9185

  • d. 0.0771

• Answer: d. 0.0771

Question 50: Normal Distribution of $X$

• Question: $X$ is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that $X$ is between 1.48 and 15.56 is:

  • a. 0.0222

  • b. 0.4190

  • c. 0.5222

  • d. 0.9190

• Answer: d. 0.9190

Question 51: Normal Distribution with Given Mean and Variance

• Question: $X$ is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that $X$ is greater than 10.52 is:

  • a. 0.0029

  • b. 0.0838

  • c. 0.4971

  • d. 0.9971

• Answer: a. 0.0029

Question 52: Probability for Specific Value of $X$

• Question: $X$ is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that $X$ equals 19.62 is:

  • a. 0.000

  • b. 0.0055

  • c. 0.4945

  • d. 0.9945

• Answer: a. 0.000

Question 53: Probability Less than 9.7

• Question: $X$ is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that $X$ is less than 9.7 is:

  • a. 0.000

  • b. 0.4931

  • c. 0.0069

  • d. 0.9931

• Answer: c. 0.0069

Question 54: $Z$ for Area to Right of 0.5

• Question: Given that $Z$ is a standard normal random variable, what is the value of $Z$ if the area to the right of $Z$ is 0.5?

  • a. 0.0000

  • b. 1.0000

  • c. 0.1915

  • d. 0.3413

• Answer: a. 0.0000

Question 55: $Z$ for Area to Left of 0.0559

• Question: Given that $Z$ is a standard normal random variable, what is the value of $Z$ if the area to the left of $Z$ is 0.0559?

  • a. 0.4441

  • b. 1.59

  • c. 0.0000

  • d. 1.50

• Answer: b. 1.59

Question 56: Exhibit 4 - Mean of $x$

• Exhibit 4: $f(x) = (1/10) e^{-x/10}$ for $x \geq 0$

• Question: The mean of $x$ is:

  • a. 0.10

  • b. 10

  • c. 100

  • d. 1,000

• Answer: b. 10

Question 57: Probability Between 3 and 6

• Question: The probability that $x$ is between 3 and 6 is:

  • a. 0.4512

  • b. 0.1920

  • c. 0.2592

  • d. 0.6065

• Answer: b. 0.1920

Question 58: Probability Less Than 5

• Question: The probability that $x$ is less than 5 is:

  • a. 0.6065

  • b. 0.0606

  • c. 0.3935

  • d. 0.9393

• Answer: c. 0.3935

Question 59: Exhibit 5 - Travel Time

• Exhibit 5: The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.

• Question: The probability that she will finish her trip in 80 minutes or less is:

  • a. 0.02

  • b. 0.8

  • c. 0.2

  • d. 1.00

• Answer: b. 0.8

Question 60: Probability Exceeding 60 Minutes

• Question: The probability that her trip will take longer than 60 minutes is:

  • a. 1.00

  • b. 0.40

  • c. 0.02

  • d. 0.600

• Answer: d. 0.600

Question 61: Probability of Exact Time

• Question: The probability that her trip will take exactly 50 minutes is:

  • a. zero

  • b. 0.02

  • c. 0.06

  • d. 0.20

• Answer: a. zero

Question 62: Exhibit 6 - Starting Salaries of MBA Graduates

• Exhibit 6: The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.

• Question: What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

  • a. 0.4772

  • b. 0.9772

  • c. 0.0228

  • d. 0.5000

• Answer: b. 0.9772

Question 63: Salary of at least $47,500

• Question: What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?

  • a. 0.4332

  • b. 0.9332

  • c. 0.0668

  • d. 0.5000

• Answer: c. 0.0668

Question 64: Percent of MBA's with Salaries Between $34,000 and $46,000

• Question: What percentage of MBA's will have starting salaries of $34,000 to $46,000?

  • a. 38.49%

  • b. 38.59%

  • c. 50%

  • d. 76.98%

• Answer: d. 76.98%

Question 65: Exponential Probability Distribution Characteristics

• Question: An exponential probability distribution:

  • a. is a continuous distribution

  • b. is a discrete distribution

  • c. can be either continuous or discrete

  • d. must be normally distributed

• Answer: a. is a continuous distribution

Question 66: Exhibit 7 - Weight of Machine Produced Items

• Exhibit 7: The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

• Question: What is the probability that a randomly selected item will weigh more than 10 ounces?

  • a. 0.3413

  • b. 0.8413

  • c. 0.1587

  • d. 0.5000

• Answer: c. 0.1587

Question 67: Probability Between 11 and 12 Ounces

• Question: What is the probability that a randomly selected item will weigh between 11 and 12 ounces?

  • a. 0.4772

  • b. 0.4332

  • c. 0.9104

  • d. 0.0440

• Answer: d. 0.0440

Question 68: Percentage of Items Weighing at Least 11.7 Ounces

• Question: What percentage of items will weigh at least 11.7 ounces?

  • a. 46.78%

  • b. 96.78%

  • c. 3.22%

  • d. 53.22%

• Answer: c. 3.22%

Question 69: Percentage Between 6.4 and 8.9 Ounces

• Question: What percentage of items will weigh between 6.4 and 8.9 ounces?

  • a. 0.1145

  • b. 0.2881

  • c. 0.1736

  • d. 0.4617

• Answer: d. 0.4617

Question 70: Probability of Exactly 8 Ounces

• Question: What is the probability that a randomly selected item weighs exactly 8 ounces?

  • a. 0.5

  • b. 1.0

  • c. 0.3413

  • d. 0.0000

• Answer: d. 0.0000

Question 71: $Z$ for Area to Right of 0.1112

• Question: $Z$ is a standard normal random variable. What is the value of $Z$ if the area to the right of $Z$ is 0.1112?

  • a. 0.3888

  • b. 1.22

  • c. 2.22

  • d. 3.22

• Answer: b. 1.22

Question 72: $Z$ for Area Between -Z and Z

• Question: $Z$ is a standard normal random variable. What is the value of $Z$ if the area between -$Z$ and $Z$ is 0.754?

  • a. 0.377

  • b. 0.123

  • c. 2.16

  • d. 1.16

• Answer: d. 1.16

Question 73: $Z$ for Area to Right of 0.9803

• Question: $Z$ is a standard normal random variable. What is the value of $Z$ if the area to the right of $Z$ is 0.9803?

  • a. -2.06

  • b. 0.4803

  • c. 0.0997

  • d. 3.06

• Answer: a. -2.06

Question 74: Probability of $Z$ Between -2.4 and -2.0

• Question: For a standard normal distribution, the probability of obtaining a $z$ value between -2.4 to -2.0 is:

  • a. 0.4000

  • b. 0.0146

  • c. 0.0400

  • d. 0.5000

• Answer: b. 0.0146

Question 75: Probability of $Z$ Less than 1.6

• Question: For a standard normal distribution, the probability of obtaining a $z$ value of less than 1.6 is:

  • a. 0.1600

  • b. 0.0160

  • c. 0.0016

  • d. 0.9452

• Answer: d. 0.9452

Question 76: Probability of $Z$ Between -1.9 and 1.7

• Question: For a standard normal distribution, the probability of obtaining a $z$ value between -1.9 to 1.7 is:

  • a. 0.9267

  • b. 0.4267

  • c. 1.4267

  • d. 0.5000

• Answer: a. 0.9267

Question 77: Exhibit 8 - Tire Life Expectancy

• Exhibit 8: The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.

• Question: What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

  • a. 0.4772

  • b. 0.9772

  • c. 0.0228

  • d. 0.5000

• Answer: b. 0.9772

Question 78: Probability of Tire Life at Least 47,500

• Question: What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

  • a. 0.4332

  • b. 0.9332

  • c. 0.0668

  • d. 0.4993

• Answer: c. 0.0668

Question 79: Percent of Tires Between 34,000 to 46,000 Miles

• Question: What percentage of tires will have a life of 34,000 to 46,000 miles?

  • a. 38.49%

  • b. 76.98%

  • c. 50%

  • d. 88.49%

• Answer: b. 76.98%

Question 80: Probability of Tire Life Exactly 47,500 Miles

• Question: What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

  • a. 0.0000

  • b. 0.9332

  • c. 0.0668

  • d. 0.4993

• Answer: a. 0.0000

Question 81: Ages of University Students

• Question: The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

  • a. It could be any value, depending on the magnitude of the standard deviation

  • b. 50%

  • c. 21%

  • d. 1.96%

• Answer: b. 50%

Question 82: Probability for $Z$ Between 1.05 and 2.13

• Question: $Z$ is a standard normal random variable. The P(1.05 < Z < 2.13) equals:

  • a. 0.8365

  • b. 0.1303

  • c. 0.4834

  • d. 0.3531

• Answer: b. 0.1303

Question 83: Probability for Z > 2.11

• Question: $Z$ is a standard normal random variable. The P(Z > 2.11) equals:

  • a. 0.4821

  • b. 0.9821

  • c. 0.5

  • d. 0.0174

• Answer: d. 0.0174

Question 84: Probability for -1.5 < Z < 1.09

• Question: $Z$ is a standard normal random variable. The P(-1.5 < Z < 1.09) equals:

  • a. 0.4322

  • b. 0.3621

  • c. 0.7953

  • d. 0.0711

• Answer: c. 0.7953

Question 85: Finding $Z$ for Area to Left 0.9382

• Question: Given that $Z$ is a standard normal random variable. What is the value of $Z$ if the area to the left of $Z$ is 0.9382?

  • a. 1.8

  • b. 1.54

  • c. 2.1

  • d. 1.77

• Answer: b. 1.54

Question 86: Finding $Z$ for Area Right 0.1401

• Question: Given that $Z$ is a standard normal random variable. What is the value of $Z$ if the area to the right of $Z$ is 0.1401?

  • a. 1.08

  • b. 0.1401

  • c. 2.16

  • d. -1.08

• Answer: a. 1.08

Question 87: Value of $Z$ for Area Between -Z and Z

• Question: Given that $Z$ is a standard normal random variable. What is the value of $Z$ if the area between –$Z$ and $Z$ is 0.754?

  • a. $\pm 1.16$

  • b. $\pm 1.96$

  • c. $\pm 2.0$

  • d. $\pm 11.6$

• Answer: a. $\pm 1.16$

Question 88: Value of $Z$ for Area Right 0.9834

• Question: Given that $Z$ is a standard normal random variable. What is the value of $Z$ if the area to the right of $Z$ is 0.9834?

  • a. 0.4834

  • b. -2.13

  • c. +2.13

  • d. zero

• Answer: b. -2.13

Question 89: Value of $Z$ for Area to Left 0.119

• Question: Given that $Z$ is a standard normal random variable. What is the value of $Z$ if the area to the left of $Z$ is 0.119?

  • a. 0.381

  • b. +1.18

  • c. -1.18

  • d. 2.36

• Answer: c. -1.18

Question 90: Value of $Z$ for Area Between -Z and Z at 0.901

• Question: Given that $Z$ is a standard normal random variable. What is the value of $Z$ if the area between -$Z$ and $Z$ is 0.901?

  • a. 1.96

  • b. -1.96

  • c. 0.4505

  • d. $\pm 1.65$

• Answer: d. $\pm 1.65$

Question 91: Normal Approximation to the Binomial Distribution

• Question: Use the normal approximation to the binomial distribution to answer the question. Fifteen percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent?

  • a. 0.0683

  • b. 0.0213

  • c. 0.0021

  • d. 0.1329

• Answer: a. 0.0683