Deck 8: Continuous Distributions

Question 1

If x is continuously 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

Answer 1

0.750

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

If x is continuously 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

Answer 3

0.375

Question 4

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

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

Question 5

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

Question 6

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

Question 7

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

Question 8

If x is continuously 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 9

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

Question 10

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 11

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

Question 12

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

Question 13

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

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

Question 14

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

Question 15

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

Question 16

If x is continuously 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 17

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

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

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 20

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

Question 21

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 22

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 23

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 24

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 25

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 26

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 27

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

A) 0.67
B) -1.25
C) 0.00
D) 1.28
E) 0.50

Question 28

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 29

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 30

If x is uniformly distributed over some interval. The mean value (μ) of x is 2 and its variance (σ²) is 1/3. The probability that x is between 2 and 2.5, P(2 $\le$ x $\le$ 2.5), is ___.

A) 0.45
B) 0.40
C) 0.35
D) 0.33
E) 0.25

Question 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 $\geq$ 24) is ___.

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

Question 39

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 40

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 41

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 42

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 43

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 44

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on 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) 1.00
B) -1.00
C) 11.00
D) -11.00
E) 0.10

Question 45

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on 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 46

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on 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 47

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 48

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 49

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 50

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) -1.25
C) 1.96
D) 1.28
E) -1.645

Question 51

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on 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 52

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 53

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

A) 0.67
B) -1.25
C) 0.00
D) 1.28
E) 0.50

Question 54

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 55

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 56

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 ___.

A) 0.0000
B) 0.3413
C) 0.0005
D) 0.0500
E) 0.6915

Question 57

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 58

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 between 30,000 and 50,000 miles?

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

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 fewer than 940 hours?

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

Question 60

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 $\textbf{ not }$ 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 61

Suppose x is uniformly distributed over some interval and the mean value (μ) of x is 2 and its variance (σ²) is 1/3. Find the probability that x is between 2 and 2.5, P(2 $\le$ x $\le$ 2.5).

Question 62

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. If the random variable x = Age is normally distributed,
a) What is the probability that a student will be younger than 16.2 years?
b) How many students are older than 16.2 years?

Question 63

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 64

If variable x is normally distributed with mean 0 and standard deviation 1, x ~ N(0,1), then the probability that x is exactly 0 is ___.

A) 0.05
B) 0.04
C) 0.02
D) 0.01
E) 0.00