Deck 6: Continuous Probability Distributions

Question 1

A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called

A) 50% of the area under the normal curve
B) continuity correction factor
C) factor of conversion
D) all of the alternatives are correct answers

Answer 1

B

Question 2

For a continuous random variable x, the probability density function fx) 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 2

D

Question 3

The z score for the standard normal distribution

A) is always equal to zero
B) can never be negative
C) can be either negative or positive
D) is always equal to the mean

Answer 3

C

Question 4

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

Question 5

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

Question 6

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

Question 7

The uniform, normal, and exponential distributions are

A) all continuous probability distributions
B) all discrete probability distributions
C) can be either continuous or discrete, depending on the data
D) all the same distributions

Question 8

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

Question 9

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

Question 10

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

Question 11

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

A) normal function
B) uniform function
C) either normal of uniform depending on the situation
D) probability density function

Question 12

The center of a normal curve is

A) always equal to zero
B) is the mean of the distribution
C) cannot be negative
D) is the standard deviation

Question 13

A normal distribution with a mean of 0 and a standard deviation of 1 is called

A) a probability density function
B) an ordinary normal curve
C) a standard normal distribution
D) none of these alternatives is correct

Question 14

In a standard normal distribution, the probability that Z is greater than zero is

A) 0.5
B) equal to 1
C) at least 0.5
D) 1.96

Question 15

A negative value of Z indicates that

A) the number of standard deviations of an observation is to the right of the mean
B) the number of standard deviations of an observation is to the left of the mean
C) a mistake has been made in computations, since Z cannot be negative
D) the data has a negative mean

Question 16

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

Question 17

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.

Question 18

The probability that a continuous random variable takes any specific value

A) is equal to zero
B) is at least 0.5
C) depends on the probability density function
D) is very close to 1.0

Question 19

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

A) normal probability distribution
B) uniform probability distribution
C) exponential probability distribution
D) Poisson probability distribution

Question 20

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

Question 21

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

Question 22

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

Question 23

In a standard normal distribution the probability of z being less than or equal zero is

A) 0.0000
B) much larger than 1
C) there is no answer to this question, since the value of the mean is not known
D) 0.5000

Question 24

Z is a standard normal random variable. The P-1.96 ≤ Z ≤ -1.4) equals

A) 0.8942
B) 0.0558
C) 0.475
D) 0.4192

Question 25

The standard deviation of a standard normal distribution

A) is always equal to zero
B) is always equal to one
C) can be any positive value
D) can be any value

Question 26

Given that Z is a standard normal random variable, what is the probability that Z ≥ -2.12?

A) 0.4830
B) 0.9830
C) 0.017
D) 0.966

Question 27

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

Question 28

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

Question 29

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

Question 30

For a standard normal distribution, the probability of z ≤ 0 is

A) zero
B) -0.5
C) 0.5
D) one

Question 31

Given that Z is a standard normal random variable, what is the probability that -2.08 ≤ Z ≤ 1.46?

A) 0.9091
B) 0.4812
C) 0.4279
D) 0.0533

Question 32

Z is a standard normal random variable. The P 1.20 ≤ Z ≤ 1.85) equals

A) 0.4678
B) 0.3849
C) 0.8527
D) 0.0829

Question 33

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.

Question 34

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

Question 35

The mean of a standard normal probability distribution

A) is 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

Question 36

Given that Z is a standard normal random variable, what is the probability that -2.51 ≤ Z ≤ -1.53?

A) 0.4950
B) 0.4370
C) 0.0570
D) 0.9310

Question 37

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

Question 38

Z is a standard normal random variable. The P -1.20 ≤ Z ≤ 1.50) equals

A) 0.0483
B) 0.3849
C) 0.4332
D) 0.8181

Question 39

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.

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

In a standard normal distribution the value of z

A) can be any value
B) cannot be negative
C) cannot be larger than 3.09
D) cannot be larger than 0.50

Question 45

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

Question 46

Z is a standard normal random variable. The PZ ≥ 2.11) equals

A) 0.4821
B) 0.9821
C) 0.5
D) 0.0174

Question 47

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

Question 48

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

Question 49

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

Question 50

The entire area under the standard normal distribution curve

A) can be any value
B) cannot be negative
C) can be any positive value
D) can be any positive value larger than 1

Question 51

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

Question 52

Use the normal approximation to the binomial distribution to answer this 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

Question 53

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

Question 54

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

Question 55

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

Question 56

Z is a standard normal random variable. The P1.05 ≤ Z ≤ 2.13) equals

A) 0.8365
B) 0.1303
C) 0.4834
D) 0.3531

Question 57

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

Question 58

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

Question 59

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

Question 60

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%

Question 61

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-3. 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

Question 62

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The expected assembly time in minutes) is

A) 16
B) 2
C) 8
D) 4

Question 63

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability of assembling the product in less than 6 minutes is

A) zero
B) 0.50
C) 0.15
D) 1

Question 64

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

Question 65

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) ±1.65

Question 66

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-3. 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

Question 67

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

Question 68

In a standard normal distribution the value of z

A) can be any value
B) cannot be negative
C) cannot be larger than 3.09
D) cannot be larger than 0.50

Question 69

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

Question 70

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is

A) 0.25
B) 0.75
C) zero
D) 1

Question 71

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

Question 72

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is

A) zero
B) 0.50
C) 0.20
D) 1

Question 73

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-3. 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

Question 74

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-2. What is the minimum weight of the middle 95% of the players?

A) 196
B) 151
C) 249
D) 190

Question 75

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

Question 76

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?

A) 28.81%
B) 0.5762%
C) 0.281%
D) 57.62%

Question 77

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

Question 78

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-2. The probability of a player weighing more than 241.25 pounds is

A) 0.4505
B) 0.0495
C) 0.9505
D) 0.9010

Question 79

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The standard deviation of assembly time in minutes) is approximately

A) 1.3333
B) 1.1547
C) 0.1111
D) 0.5773

Question 80

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-2. The probability of a player weighing less than 250 pounds is

A) 0.4772
B) 0.9772
C) 0.0528
D) 0.5000