Deck 6: Continuous Distributions

Question 1

In a standard normal distribution, if the area under curve to the right of a z value is 0.10, then the area to the left of the same z value is -0.10.

Answer 1

False

Question 2

Normal distribution is a skewed distribution with its tails extending to infinity on either side of the mean.

Answer 2

False

Question 3

A uniform continuous distribution is also referred to as a rectangular distribution.

Answer 3

True

Question 4

If the probability of a binomial distribution was considering values that were greater than 14, then the correction for continuity would start at 13.5.

Question 5

If arrivals at a bank followed a Poisson distribution, then the time between arrivals would follow a binomial distribution.

Question 6

The area of the rectangle depicting a uniform distribution is always equal to the mean of the distribution.

Question 7

The height of the rectangle depicting a uniform distribution is the probability of each outcome and it is the same for all of the possible outcomes.

Question 8

The normal approximation for binomial distribution can be used when n=10 and p=1/5.

Question 9

A z score is the number of standard deviations that a value of a random variable is above or below the mean.

Question 10

A correction for continuity must be made when approximating the binomial distribution problems using a normal distribution.

Question 11

The z distribution is a normal distribution with a mean of zero and a standard deviation of one.

Question 12

Correcting for continuity is necessary when a researcher is using a discrete distribution to estimate probabilities from a continuous distribution.

Question 13

Binomial distributions in which the sample sizes are large may be approximated by a Poisson distribution.

Question 14

The area of the rectangle depicting a uniform distribution is always equal to one.

Question 15

Many human characteristics, such as height and weight, and many variable measurements, such as household insurance and cost per square metre of rental space, are normally distributed.

Question 16

If the probability of a binomial distribution was considering values that were less than 14, then the correction for continuity would start at 13.5.

Question 17

For an exponential distribution, the mean is always equal to its variance.

Question 18

A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

Question 19

The area under the standard normal distribution between -1 and 1 is twice the area between 0 and 1.

Question 20

Since a normal distribution curve extends from minus infinity to plus infinity, the area under the curve is infinity.

Question 21

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then P(x $\le$ 11)is ___.

A)0.750
B)0.000
C)0.333
D)0.500
E)1.000

Question 22

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the mean of this distribution is ___.

A)10
B)20
C)5
D)0
E)unknown

Question 23

If x, the time (in minutes)to complete an oil change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the standard deviation of this distribution is ___.

A)unknown
B)8.33
C)0.833
D)2.89
E)1.89

Question 24

Suppose the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 $\le$ x $\le$ 140), then the height of this distribution, f(x), is __________________.

A)1/90
B)1/50
C)1/140
D)1/200
E)1/500

Question 25

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then P(x $\ge$ 10)is ___.

A)0.750
B)0.000
C)0.333
D)0.500
E)0.900

Question 26

If x, the time (in minutes)to complete an oil change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the mean of this distribution is ___.

A)50
B)25
C)10
D)15
E)5

Question 27

If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 $\le$ x $\le$ 140), then the standard deviation of this distribution is approximately __________________.

A)4.16
B)50
C)14.4
D)7.07
E)28.2

Question 28

The standard deviation of an exponential distribution is equal to 1/λ.

Question 29

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the probability, P(9 $\le$ x $\le$ 11), is ___.

A)0.250
B)0.500
C)0.333
D)0.750
E)1.000

Question 30

If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 $\le$ x $\le$ 140), then the mean of this distribution is __________________.

A)115
B)230
C)45
D)70
E)unknown

Question 31

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the standard deviation of this distribution is approximately___.

A)4.00
B)1.33
C)1.15
D)2.00
E)1.00

Question 32

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then P(x < 7)is ___.

A)0.500
B)0.000
C)0.375
D)0.250
E)1.000

Question 33

The exponential distribution is especially useful in queuing problems to analyze the interarrival times.

Question 34

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the probability, P(10.0 $\le$ x $\le$ 11.5), is ___.

A)0.250
B)0.333
C)0.375
D)0.500
E)0.750

Question 35

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the probability, P(13 $\le$ x $\le$ 15), is ___.

A)0.250
B)0.500
C)0.375
D)0.000
E)1.000

Question 36

For an exponential distribution, the mean and the median are equal.

Question 37

If x, the time (in minutes)to complete an oil change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the height of this distribution, f(x), is ___.

A)1/10
B)1/20
C)1/30
D)12/50
E)1/60

Question 38

The mean of an exponential distribution is equal to 1/λ.

Question 39

The exponential distribution is a continuous distribution that is closely related to the Poisson distribution.

Question 40

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the height of this distribution, f(x), is ___.

A)1/8
B)1/4
C)1/12
D)1/20
E)1/24

Question 41

If x, the time (in minutes)to complete an oil change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in 33 to 35 minutes, inclusively, i.e., P(33 $\le$ x $\le$ 35)is ___.

A)0.5080
B)0.000
C)0.375
D)0.200
E)1.000

Question 42

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ( $\sigma$ )of 1.What is P(1.3 < z < 2.3)?

A)0.4032
B)0.9032
C)0.4893
D)0.0861
E)0.0086

Question 43

The area to the left of the mean in any normal distribution is equal to ___.

A)the mean
B)1
C)the variance
D)0.5
E)-0.5

Question 44

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ()of 1.What is P(z > -1.1)?

A)0.36432
B)0.8643
C)0.1357
D)-0.1357
E)-0.8643

Question 45

If x, the time (in minutes)to complete an change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in 21.75 to 24.25 minutes, inclusively, i.e., P(21.75 $\le$ x $\le$ 24.25)is ___.

A)0.250
B)0.333
C)0.375
D)0.000
E)1.000

Question 46

If x, the time (in minutes)to complete an oil change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job will be completed 24 minutes or more, i.e., P(x $\ge$ 24)is ___.

A)0.100
B)0.000
C)0.333
D)0.600
E)1.000

Question 47

If x, the time (in minutes)to complete an oil change job at a certain auto station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in less than or equal to 22 minutes, i.e., P(x $\le$ 22)is ___.

A)0.200
B)0.300
C)0.000
D)0.250
E)1.000

Question 48

Suppose x is a normal random variable with mean ( $\mu$ )equal to 60 and standard deviation ( $\sigma$ )of 2.If the z score was calculated to be -1.3, what is the value of x?

A)58.7
B)61.3
C)62.6
D)57.4
E)54.7

Question 49

If x, the time (in minutes)to complete an oil change job at a certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in less than 17 minutes, i.e., P(x < 17)is ___.

A)0.500
B)0.300
C)0.000
D)0.250
E)1.000

Question 50

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ( $\sigma$ )of 1.What is P(z < -2.1)?

A)0.4821
B)-0.4821
C)0.9821
D)0.0179
E)-0.0179

Question 51

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ( $\sigma$ )of 1.What is P(z > 2.4)?

A)0.4918
B)0.9918
C)0.0082
D)0.4793
E)0.0820

Question 52

Let z be a normal random variable with mean 0 and standard deviation 1.The 75^th percentile of z is most closely reflected by ___.

A)0.6700
B)-1.254
C)0.0000
D)1.2800
E)0.5000

Question 53

Let z be a normal random variable with mean ( $\mu$ )equal to 0 and standard deviation ( $\sigma$ )of 1.What is P(z < 1.3)?

A)0.4032
B)0.9032
C)0.0968
D)0.3485
E)0.5485

Question 54

The total area underneath any normal curve is equal to ___.

A)the mean
B)one
C)the variance
D)the coefficient of variation
E)the standard deviation

Question 55

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ()of 1.The 50^th percentile of z is most closely reflected by ___.

A)0.6700
B)-1.254
C)0.0000
D)1.2800
E)0.5000

Question 56

The normal distribution is an example of ___.

A)a discrete distribution
B)a continuous distribution
C)a bimodal distribution
D)an exponential distribution
E)a binomial distribution

Question 57

If x is a normal random variable with mean ( $\mu$ )equal to 80 and a standard deviation ( $\sigma$ )of 5, the z score for x = 88 is ___.

A)1.8
B)-1.8
C)1.6
D)-1.6
E)8.0

Question 58

A z score is the number of ___ that a value, x, is from the mean.

A)variances
B)standard deviations
C)units
D)miles
E)minutes

Question 59

Within a range of z scores from -1 to +1, you can expect to find ___ per cent of the values in a normal distribution.

A)95
B)99
C)68
D)34
E)100

Question 60

Suppose x is a normal random variable with mean ( $\mu$ )equal to 60 and standard deviation ( $\sigma$ )of 2.If the z score was calculated to be 3.4, what is the value of x?

A)63.4
B)56.6
C)68.6
D)53.2
E)66.8

Question 61

The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last fewer than 940 hours?

A)0.3849
B)0.8849
C)0.1151
D)0.6151
E)0.6563

Question 62

The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last longer than 1,150 hours?

A)0.4987
B)0.9987
C)0.0013
D)0.5013
E)0.5513

Question 63

Let x be a binomial random variable with n=35 and p=.20.If we use the normal distribution to approximate probabilities for this, we would use a mean of _______.

A)35
B)20
C)70
D)7
E)3.5

Question 64

Suppose the total time to fill a routine prescription at a local pharmacy averages 35 minutes starting from the time the physician places the order to the time it is dispensed.Assume the standard deviation is 11 minutes.The z-score for x = 46 is ________.

A)1.0
B)-1.0
C)11
D)-11
E).10

Question 65

The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last less than 1,100 hours?

A)0.4772
B)0.9772
C)0.0228
D)0.5228
E)0.5513

Question 66

Suppose the total time to fill a routine prescription at a local pharmacy averages 35 minutes starting from the time the physician places the order to the time it is dispensed.Assume the standard deviation is 11 minutes.A z score of 3.4 was calculated.What is the value of x?

A)37.4
B)72.4
C)0.00
D)68.0
E)20.8

Question 67

Suppose the total time to fill a routine prescription at a local pharmacy averages 35 minutes starting from the time the physician places the order to the time it is dispensed.Assume the standard deviation is 11 minutes and a z score of 0 was calculated.What is the value of x?

A)-35.0
B)0.0
C)70.0
D)35.0
E)-1.0

Question 68

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 kilometres and a standard deviation of 5000 kilometres.What is the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 kilometres?

A)0.5000
B)0.4772
C)0.9544
D)0.9772
E)1.0000

Question 69

A recent market study has determined that the probability that a young adult would be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults, the probability that exactly 5 will be willing to try this new service is _________, and the approximate probability (using the normal distribution is)_________.

A)0.251; 0.246
B)0.246; 0.242
C)0.246; 0.248
D)0.249; 0.251
E)0.248; 0.246

Question 70

Let x be a binomial random variable with n=50 and p=.3.If we use the normal distribution to approximate probabilities for this, a correction for continuity should be made.To find the probability of more than 15 successes, we should find _______.

A)P(x>15.5)
B)P(x>15)
C)P(x>14.5)
D)P(x<14.5)
E)P(x < 15)

Question 71

A recent market study has determined that the probability that a young adult would be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults, the approximate probability that at least 2 but no more than 3 will be willing to try this new service is _________.

A)0.1575
B)0.1612
C)0.1775
D)0.1812
E)0.1975

Question 72

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 kilometres and a standard deviation of 5000 kilometres.What is the probability that a randomly selected tire of this brand has a life of at most 30,000 kilometres?

A)0.5000
B)0.4772
C)0.0228
D)0.9772
E)1.0000

Question 73

Let x be a binomial random variable with n=50 and p=.3.The probability of less than or equal to 13 successes, when using the normal approximation for binomial is most closely reflected by ________.

A)-0.6172
B)0.3086
C)3.240
D)0.3217
E)-0.23224

Question 74

Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20.Determine the value of x such that 60% of the values are greater than x.

A)404.5
B)395.5
C)405.0
D)395.0
E)415.0

Question 75

Most graduate business schools require applicants to take the GMAT.Scores on this test are approximately normally distributed with a mean of 545 points and a standard deviation of 100 points.What score do you need to be in the top 5% (approximately the scores needed for top schools)?

A)718
B)716
C)714
D)712
E)710

Question 76

Completion time (from start to finish)of a building remodelling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.To be 99% sure that we will not be late in completing the project, we should request a completion time of ___ work-days.

A)211
B)207
C)223
D)200
E)250

Question 77

Within a range of z scores from -2 to +2, you can expect to find ___ per cent of the values in a normal distribution.

A)95
B)99
C)68
D)34
E)100

Question 78

Suppose the total time to fill a routine prescription at a local pharmacy averages 35 minutes starting from the time the physician places the order to the time it is dispensed.Assume the standard deviation is 11 minutes.A z score of -1.3 was calculated.What is the value of x?

A)20.7
B)0.0
C)-14.3
D)14.3
E)-20.7

Question 79

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 kilometres and a standard deviation of 5000 kilometres.What is the probability that a randomly selected tire of this brand has a life of at least 50,000 kilometres?

A)0.0228
B)0.9772
C)0.5000
D)0.4772
E)1.0000

Question 80

Completion time (from start to finish)of a building remodelling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.The probability that the project will be completed within 185 work-days is ___.

A)0.0668
B)0.4332
C)0.5000
D)0.9332
E)0.9950