Deck 6: Continuous Distributions

Question 1

The standard normal distribution is also called a finite distribution because its mean is zero and standard deviation one,always.

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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 11

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.

Question 12

Solve for probabilities in a continuous uniform distribution.

Question 13

Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

Question 14

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

Question 15

A standard normal distribution has a mean of zero and a standard deviation of one.

Question 16

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

Question 17

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 18

Solve for probabilities in a normal distribution using z scores and for the mean,the standard deviation,or a value of x in a normal distribution when given information about the area under the normal curve.

Question 19

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

Question 20

Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

Question 21

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 22

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 23

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 24

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 25

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 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 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 28

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 29

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 30

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 ___.

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

Question 31

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 32

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 33

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 34

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 35

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 36

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 37

If a continuous random variable x is uniformly distributed over the interval 8 to 12,inclusively,then P(x = exactly 10)is ___.

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

Question 38

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 39

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 40

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 25 to 28 minutes,inclusively,i.e. ,P(25 $\le$ x $\le$ 28)is ___.

A)0.250
B)0.500
C)0.300
D)0.750
E)81.000

Question 41

Let z be a normal random variable with mean 0 and standard deviation 1.What is P(z < 1.3)?

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

Question 42

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

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

Question 43

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

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

Question 44

Let z be a normal random variable with mean 0 and standard deviation 1.The 50^th percentile of z is ___.

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

Question 45

If x is a normal random variable with mean 80 and standard deviation 5,the z score for x = 88 is ___.

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

Question 46

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 47

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 48

Suppose x is a normal random variable with mean 60 and standard deviation 2.A z score was calculated for a number,and the z score is -1.3.What is x?

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

Question 49

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

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

Question 50

A standard normal distribution has the following characteristics:

A)the mean and the variance are both equal to 1.
B)the mean and the variance are both equal to 0.
C)the mean is equal to the variance.
D)the mean is equal to 0 and the variance is equal to 1.
E)the mean is equal to the standard deviation.

Question 51

Let z be a normal random variable with mean 0 and standard deviation 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 52

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

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

Question 53

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

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

Question 54

Let z be a normal random variable with mean 0 and standard deviation 1.The 90^th percentile of z is ___.

A)1.645
B)-1.254
C)1.960
D)1.280
E)1.650

Question 55

Let z be a normal random variable with mean 0 and standard deviation 1.What is P(-2.25 < z < -1.1)?

A)0.3643
B)0.8643
C)0.1235
D)0.4878
E)0.5000

Question 56

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 1100 hours?

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

Question 57

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 58

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 59

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 1150 hours?

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

Question 60

Suppose x is a normal random variable with mean 60 and standard deviation 2.A z score was calculated for a number,and the z score is 3.4.What is x?

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

Question 61

The average time between phone calls arriving at a call centre is 30 seconds.Assuming that the time between calls is exponentially distributed,find the probability that less than two minutes elapse between calls.

A)0.018
B)0.064
C)0.936
D)0.982
E)1.000

Question 62

On Saturdays,cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval.The probability that at least 2 minutes will elapse between car arrivals is ___.

A)0.0000
B)0.4493
C)0.1353
D)1.0000
E)1.0225

Question 63

Let x be a binomial random variable with n=20 and p=.8.If we use the normal distribution to approximate probabilities for this,we would use a mean of ___.

A)20
B)16
C)3.2
D)8
E)5

Question 64

On Saturdays,cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval.The probability that less than 10 minutes will elapse between car arrivals is ___.

A)0.8465
B)0.9817
C)0.0183
D)0.1535
E)0.2125

Question 65

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 66

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 67

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 68

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

Question 69

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 70

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 71

At a certain workstation in an assembly line,the time required to assemble a component is exponentially distributed with a mean time of 10 minutes.Find the probability that a component is assembled in 3 to 7 minutes.

A)0.5034
B)0.2592
C)0.2442
D)0.2942
E)0.5084

Question 72

The average time between phone calls arriving at a call centre is 30 seconds.Assuming that the time between calls is exponentially distributed,find the probability that more than a minute elapses between calls.

A)0.135
B)0.368
C)0.865
D)0.607
E)0.709

Question 73

The net profit of an investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000.The probability that the investor's net gain will be at least $5,000 is ___.

A)0.1859
B)0.3413
C)0.8413
D)0.4967
E)0.5000

Question 74

Let x be a binomial random variable with n=20 and p=.8.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 12 successes,we should find ___.

A)P(x>12.5)
B)P(x>12)
C)P(x>11.5)
D)P(x<11.5)
E)P(x < 12)

Question 75

The net profit from a certain investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000.The probability that the investor will not have a net loss is ___.

A)0.4772
B)0.0228
C)0.9544
D)0.9772
E)1.0000

Question 76

At a certain workstation in an assembly line,the time required to assemble a component is exponentially distributed with a mean time of 10 minutes.Find the probability that a component is assembled in 7 minutes or less.

A)0.349
B)0.591
C)0.286
D)0.714
E)0.5034

Question 77

For an exponential distribution with a lambda (λ)equal to 4,the standard deviation is equal to ___.

A)4
B)0.5
C)0.25
D)1
E)16

Question 78

The exponential distribution is an example of ___.

A)a discrete distribution
B)a continuous distribution
C)a bimodal distribution
D)a normal distribution
E)a symmetrical distribution