Deck 6: Continuous Probability Distributions

Question 1

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable follows a(n) _____ distribution.

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

Answer 1

uniform

Question 2

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product between 7 and 9 minutes is _____.

A) 0
B) .50
C) .20
D) 1

Answer 2

.50

Question 3

The mean, median, and mode have the same value for which of the following probability distributions?

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

Answer 3

normal

Question 4

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 minutes or more is _____.

A) .25
B) .75
C) 0
D) 1

Question 5

The probability distribution that can be described by just one parameter is the _____ distribution.

A) uniform
B) normal
C) exponential
D) continuous

Question 6

There is a lower limit but no upper limit for a random variable that follows the _____ probability distribution.

A) uniform
B) normal
C) exponential
D) binomial

Question 7

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) either different or the same depending on the magnitude of the standard deviation
D) None of the answers is correct.

Question 8

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 9

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in less than 6 minutes is _____.

A) 0
B) .50
C) .15
D) 1

Question 10

For a uniform probability density function, the height of the function _____.

A) cannot be larger than1
B) is the same for each value of x
C) is different for various values of x
D) decreases as x increases

Question 11

For any continuous random variable, the probability that the random variable takes on exactly a specific value is _____.

A) 1
B) .50
C) any value between 0 and 1
D) 0

Question 12

The form of the continuous uniform probability distribution is _____.

A) triangular
B) rectangular
C) bell-shaped
D) a series of vertical lines

Question 13

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

A) .75
B) .5
C) .05
D) 1

Question 14

What type of function defines the probability distribution of ANY continuous random variable?

A) Normal distribution function only
B) Uniform distribution function only
C) Both the normal distribution function and the uniform distribution function
D) Probability density function

Question 15

The probability density function for a uniform distribution ranging between 2 and 6 is _____.

A) 4
B) undefined
C) any positive value
D) .25

Question 16

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) both the probability at a given value of x and the area under the curve at x
D) the height of the function at x

Question 17

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The expected assembly time (in minutes) is _____.

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

Question 18

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability density function has what value in the interval between 6 and 10?

A) .25
B) 4.00
C) 5.00
D) 0

Question 19

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

Question 20

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n) _____ probability distribution.

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

Question 21

The mean of a standard normal probability distribution _____.

A) is always equal to 1
B) can be any value as long as it is positive
C) can be any value
D) None of the answers is correct.

Question 22

Assume z is a standard normal random variable. Then P(-1.5 ≤ z ≤ 1.09) equals _____.

A) .4322
B) .3621
C) .7953
D) .0711

Question 23

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 the answers is correct.

Question 24

Assume z is a standard normal random variable. Then P(-1.96 ≤ z ≤ -1.4) equals _____.

A) .8942
B) .0558
C) .475
D) .4192

Question 25

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 26

Assume z is a standard normal random variable. Then P(-1.20 ≤ z ≤ 1.50) equals _____.

A) .0483
B) .3849
C) .4332
D) .8181

Question 27

A standard normal distribution is a normal distribution with _____.

A) a mean of 1 and a standard deviation of 0
B) a mean of 0 and a standard deviation of 1
C) any mean and a standard deviation of 1
D) any mean and any standard deviation

Question 28

The standard deviation of a standard normal distribution _____.

A) is always equal to 0
B) is always equal to 1
C) can be any positive value
D) can be any value

Question 29

For a standard 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 30

Assume z is a standard normal random variable. Then P(1.41 < z < 2.85) equals _____.

A) .4772
B) .3413
C) .8285
D) None of the answers is correct.

Question 31

For the standard normal probability distribution, the area to the left of the mean is _____.

A) -.5
B) 0.5
C) any value between 0 and 1
D) 1

Question 32

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

A) 0
B) -.5
C) .5
D) 1

Question 33

Which of the following is NOT a characteristic of the normal probability distribution?

A) The graph of the curve is the shape of a rectangle.
B) The total area under the curve is always equal to 1.
C) The random variable assumes a value within plus or minus three standard deviations of its mean 99.72% of the time.
D) The mean is equal to the median, which is also equal to the mode.

Question 34

Which of the following is NOT a characteristic of the normal probability distribution?

A) The mean, median, and 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 35

Assume z is a standard normal random variable. Then P(1.20 ≤ z ≤ 1.85) equals _____.

A) .4678
B) .3849
C) .8527
D) .0829

Question 36

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 37

Assume z is a standard normal random variable. Then P(1.05 ≤ z ≤ 2.13) equals _____.

A) .8365
B) .1303
C) .4834
D) None of the answers is correct.

Question 38

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 39

A normal probability distribution _____.

A) is a continuous probability distribution
B) is a discrete probability distribution
C) can be either continuous or discrete
D) always has a standard deviation of 1

Question 40

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The standard deviation of assembly time (in minutes) is approximately _____.

A) .33
B) .13
C) 16
D) None of the answers is correct.

Question 41

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 42

For a standard normal distribution, the probability of obtaining a z value between -1.9 and 1.7 is _____.

A) .9267
B) .4267
C) 1.4267
D) .5000

Question 43

Suppose 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
B) .4931
C) .0069
D) .9931

Question 44

Excel's NORM.DIST function can be used to compute _____.

A) cumulative probabilities for a standard normal z value
B) the standard normal z value given a cumulative probability
C) cumulative probabilities for a normally distributed x value
D) the normally distributed x value given a cumulative probability

Question 45

Suppose 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) .0029
B) .0838
C) .4971
D) .9971

Question 46

Suppose 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) .0222
B) .4190
C) .5222
D) .9190

Question 47

Suppose 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
B) .0055
C) .4945
D) .9945

Question 48

Excel's NORM.S.DIST function can be used to compute _____.

A) cumulative probabilities for a standard normal z value
B) the standard normal z value given a cumulative probability
C) cumulative probabilities for a normally distributed x value
D) the normally distributed x value given a cumulative probability

Question 49

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is .9382?

A) 1.8
B) 1.54
C) 2.1
D) 1.77

Question 50

Excel's NORM.INV function can be used to compute _____.

A) cumulative probabilities for a standard normal z value
B) the standard normal z value given a cumulative probability
C) cumulative probabilities for a normally distributed x value
D) the normally distributed x value given a cumulative probability

Question 51

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is _____.

A) .1600
B) .0160
C) .0016
D) .9452

Question 52

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1401?

A) 1.08
B) .1401
C) 2.16
D) -1.08

Question 53

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1112?

A) .3888
B) 1.22
C) 2.22
D) 3.22

Question 54

Assume z is a standard normal random variable. What is the value of z if the area between -z and z is .754?

A) .377
B) .123
C) 2.16
D) 1.16

Question 55

Assume z is a standard normal random variable. Then P(z ≥ 2.11) equals _____.

A) .4821
B) .9821
C) .5
D) .0174

Question 56

Excel's NORM.S.INV function can be used to compute _____.

A) cumulative probabilities for a standard normal z value
B) the standard normal z value given a cumulative probability
C) cumulative probabilities for a normally distributed x value
D) the normally distributed x value given a cumulative probability

Question 57

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

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

Question 58

Assume z is a standard normal random variable. What is the value of z if the area to the right of z is .9803?

A) -2.06
B) .4803
C) .0997
D) 3.06

Question 59

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 60

For a standard normal distribution, the probability of obtaining a z value between -2.4 and -2.0 is _____.

A) .4000
B) .0146
C) .0400
D) .5000

Question 61

The average starting salary of this year's MBA students is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and maximum starting salaries of the middle 95% of MBA graduates?

Question 62

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 63

A property of the exponential distribution is that the mean equals the _____.

A) mode
B) median
C) variance
D) standard deviation

Question 64

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and standard deviation.

Question 65

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if _____ is desired.

A) a probability
B) a cumulative probability
C) the expected value
D) the correct answer

Question 66

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked" large" and shrimp that weigh less than 0.47 ounce each into packages marked "small"; the remainder are packed in "medium" size packages. If a day's catch showed that 19.77% of the shrimp were large and 6.06% were small, determine the mean and standard deviation for the shrimp weights. Assume that the shrimps' weights are normally distributed.

Question 67

Excel's EXPON.DIST function has how many inputs?

A) 2
B) 3
C) 4
D) 5

Question 68

All of the following distributions are symmetric EXCEPT the _____ distribution.

A) uniform
B) normal
C) exponential
D) standard normal

Question 69

Suppose x is a normally distributed random variable with a mean of 50 and a standard deviation of 5. Use Excel to calculate the following:
a.
P(x ≤ 45)
b.
P(45 ≤ x ≤ 55)
c.
P(x ≥ 55)
d.
x value with 0.20 in the lower tail
e.
x value with 0.01 in the upper tail
​

Question 70

In grading eggs into small, medium, and large, Linda Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and standard deviation for the eggs' weights. Assume that the distribution of the weights is normal.

Question 71

About 95.4% of the values of a normal random variable are within approximately how many standard deviations of its mean?

A) ±1.7
B) ±2
C) ±2.5
D) ±3

Question 72

The skewness measure for exponential distributions is _____.

A) 0
B) 1
C) 2
D) 3

Question 73

Exponential distributions _____.

A) are skewed to the left
B) are skewed to the right
C) can be skewed to the left or right
D) are not skewed

Question 74

Excel's EXPON.DIST function can be used to compute _____.

A) exponents
B) exponential probabilities only
C) cumulative exponential probabilities only
D) both exponential and cumulative exponential probabilities