Deck 6: Continuous Distributions

Question 1

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

Answer 1

True

Question 2

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 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

The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

Question 5

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 6

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

Question 7

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

Question 8

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

Question 9

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 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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 18

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

Question 19

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

Question 20

Many human characteristics such as height and weight and many variables such as household insurance and cost per square foot of rental space are normally distributed.

Question 21

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 22

If x, the time (in minutes)to complete an oil change job at 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 23

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 24

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 25

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 26

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 27

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

Question 28

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

Question 29

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 30

If x, the time (in minutes)to complete an oil change job at 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 31

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

Question 32

If x, the time (in minutes)to complete an change job at 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 33

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 P(x = exactly 100)is __________________.

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

Question 34

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 __________________.

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

Question 35

If x, the time (in minutes)to complete an change job at 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 36

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

Question 37

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 38

If x, the time (in minutes)to complete an oil change job at 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

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

Question 40

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 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 most closely reflected by ____________.

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

Question 43

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 44

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 45

If x, the time (in minutes)to complete an change job at 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 46

Let z be a normal random variable with mean 0 and standard deviation 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 47

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 48

Let z be a normal random variable with mean 0 and standard deviation 1.Which of these most closely reflects P(-2.25 < z < -1.1)?

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

Question 49

If x, the time (in minutes)to complete an change job at 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 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 51

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 52

If x, the time (in minutes)to complete an change job at 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 53

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 54

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 55

If x, the time (in minutes)to complete an change job at 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 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 56

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 57

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 58

Let z be a normal random variable with mean 0 and standard deviation 1.The 90^th percentile of z is most closely reflected by ____________.

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

Question 59

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

A)0.3643
B)0.8643
C)0.1357
D)-0.1357
E)-0.8643

Question 60

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 61

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 62

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 was calculated for a number, and the z score is 3.4.What is x?

A)37.4
B)72.4
C)0.00
D)68.0
E)2.0.8

Question 63

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 64

Completion time (from start to finish)of a building remodeling 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 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.Which most closely reflects 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 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 and the z score is -1.3.What is x?

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

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 most likely 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

Assuming an equal chance of a new baby being a boy or a girl (that is, p= 0.5), we would like to find the probability of 40 or more of the next 100 births at a local hospital will be boys.Using the normal approximation for binomial with a correction for continuity, we should use the z-score _______

A)0.4
B)-2.1
C)0.6
D)2
E)-1.7

Question 69

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.Which most closely reflects 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 70

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000.The probability that the investor will not have a net loss is _____________.

A)0.4938
B)0.0062
C)0.9938
D)0.5062
E)0.0000

Question 71

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.Which most closely reflects 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 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 miles and a standard deviation of 5000 miles.What is the probability that a randomly selected tire of this brand has a life of at most 30,000 miles?

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=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 74

Completion time (from start to finish)of a building remodeling 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 75

For the normal approximation to be a good approximation for binomial distribution, n*p must be greater than ___________.

A)50
B)5
C)0.5
D)0.05
E)0

Question 76

The probability that a call to an emergency help line is answered in less than 10 seconds is 0.8.Assume that the calls are independent of each other.Using the normal approximation for binomial with a correction for continuity, the probability that at least 75 of 100 calls are answered within 10 seconds is approximately _______

A)0.8
B)0.1313
C)0.5235
D)0.9154
E)0.8687

Question 77

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 miles and a standard deviation of 5000 miles.Which probability most closely reflects that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?

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

Question 78

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 miles and a standard deviation of 5000 miles.What is the probability that a randomly selected tire of this brand has a life of at least 50,000 miles?

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

Question 79

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 the z score is 0.What is x?

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

Question 80

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000.The probability that the investor's net gain will be at least $2,000 is most closely reflected by _____________.

A)0.0000
B)0.3413
C)0.6915
D)0.0500
E)0.5000