Deck 5: Continuous Random Variables

Question 1

For a continuous distribution,P(X ≤ 100)= P(X < 100).

Answer 1

True

Question 2

The mean of a standard normal distribution is always equal to 1.

Answer 2

False

Question 3

The number of defective pencils in a lot of 1000 pencils can be modeled using a continuous probability distribution.

Answer 3

False

Question 4

A continuous random variable may assume only integer values in a given interval.

Question 5

If the random variable of x is normally distributed,68.26% of all possible observed values of x will be within two standard deviations of the mean.

Question 6

The z value tells us the number of standard deviations that a value x is from the mean.

Question 7

The exponential probability distribution is used to model a continuous random variable.

Question 8

The standard deviation of a standard normal distribution is always equal to 1.

Question 9

A uniform distribution f(x)is a continuous probability distribution which says the probability that x is in any 2 intervals of equal length is the same.

Question 10

The mean and median are the same for a normal distribution.

Question 11

The mean and median are the same for an exponential distribution.

Question 12

In a statistical study,the random variable X = 1,if the house is colonial,and X = 0 if the house is not colonial,then it is appropriate to model this variable with a continuous probability distribution.

Question 13

For a binomial probability experiment,with n = 150 and p = .2,it is appropriate to use the normal approximation to the binomial distribution.

Question 14

The height of a probability curve f(x)at a particular point indicates the value of a probability for a given value of a random variable x.

Question 15

The actual weight of hamburger patties can be modeled using a continuous probability distribution is an example of a continuous random variable.

Question 16

The normal probability distribution is a discrete probability distribution.

Question 17

The mean life of pair of shoes is 40 months with a standard deviation of 8 months.If the life of the shoes is normally distributed,how many pairs of shoes out of one million will need replacement before 36 months?

A)500,000
B)808,500
C)191,500
D)308,500
E)705,100

Question 18

A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is called a uniform probability distribution.

Question 19

All continuous random variables are normally distributed.

Question 20

For a continuous distribution,the probability that the random variable of interest assumes a one specific value is zero.

Question 21

If the random variable of x is normally distributed,____% of all possible observed values of x will be within three standard deviations of the mean.

A)68.26
B)95.44
C)99.73
D)100
E)Cannot be determined without knowing the actual mean and standard deviation.

Question 22

Which of the following statements is not a property of the normal probability distribution?

A)The normal distribution is symmetric.
B)95.44% of all possible observed values of the random variable x are within three standard deviations of the population mean.
C)The mean,median,and mode are equal.
D)The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean.
E)68.28% of all possible observed values of the random variable x are within one standard deviation of the population mean.

Question 23

The normal approximation of the binomial distribution is appropriate when:

A)np ≥ 5
B)nq ≥ 5
C)np ≤ 5
D)nq ≤ 5 and np ≤ 5
E)np ≥ 5 and nq ≥ 5

Question 24

A study shows that employees that begin their work day at 9:00 a.m.vary their times of arrival uniformly from 8:40 a.m.to 9:30 a.m.The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:

A)0.4
B)0.2
C)0.1
D)0.3
E)0.167

Question 25

Which one of the following variables could be modeled using a continuous probability distribution?

A)The number of students in a university course.
B)The number of coffees you buy during a school year.
C)The amount of time you wait in line to buy a coffee.
D)The number of time somebody sneezes during a 1 hour class.
E)The number of times somebody shaves during one week.

Question 26

The relationship between the standard normal random variable z and normal random variable X is that:

A)Only the normal random variable X is continuous.
B)Only the standard normal variable z is continuous.
C)The standard normal variable z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
D)The values of the standard normal random variable z cannot be negative.
E)The values of the normal random variable X cannot be negative.

Question 27

A student's grade on an examination was transformed to a z value which is negative.Therefore,we know that the student scored:

A)Higher than 16% of the class
B)Higher than 45% of the class
C)Above the first quartile
D)Lower than 16% of the class
E)Below the mean

Question 28

The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

A)less than
B)greater than
C)equal to
D)always equal to
E)sometimes equal to

Question 29

A standard normal distribution has a mean of _____ and standard deviation of _____.

A)zero;zero
B)zero;one
C)one;one
D)one;zero
E)zero;three

Question 30

A property of continuous probability distributions is that:

A)Like discrete random variables,the probability distribution can be approximated by a smooth curve.
B)Probabilities for continuous variables can be approximated using discrete random variables.
C)Unlike discrete random variables,probabilities can be found using tables.
D)Unlike discrete random variables,the probability that a continuous random variable equals a specific value is zero;that is,P(X = x)= 0.
E)Unlike discrete random variables,probabilities for continuous random variables can sum to a value greater than 1.

Question 31

We calculated the value of z for a specific box of this brand of cereal and the z value was negative.This negative z value indicates that:

A)We made a mistake in our calculations,as z must always be a nonnegative number.
B)The fill weight exceeds 910 grams.
C)The fill weight is less than 910 grams
D)The fill weight is equal to 910 grams
E)The fill weight may be more or less than 910 grams depending on the value of the standard deviation.

Question 32

Let X be a binomial random variable with n = 150 and p = 0.3.Approximate P(X $\geq$
50))

A)0.7881
B)0.9909
C)0.2119
D)0.0091
E)0.5644

Question 33

If we select one box of cereal at random from this population,what is the probability that it will weigh less than 900 grams?

A)4772
B)9772
C)9544
D)0456
E)0228

Question 34

More than 33.2?

A)0.4332
B)0.0668
C)0.9332
D)0.8664
E)0.1336

Question 35

If the wages of workers for a given company are normally distributed with a mean of $15 per hour,then the proportion of the workers earning more than $13 per hour:

A)Is greater than the proportion earning less than $13 per hour.
B)Is greater than the proportion earning less than $18 per hour.
C)Is less than 50%.
D)Is less than the proportion earning more than the mean wage.
E)Is less than the proportion earning more than $14 per hour.

Question 36

Less than 33.2?

A)0.4332
B)0.0668
C)0.9332
D)0.8664
E)0.1336

Question 37

The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

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

Question 38

The price-to-earnings ratio for firms in a given industry is distributed according to normal distribution.In this industry,a firm with a standard normal variable value of z = 1:

A)Has an above average price-to-earning ratio.
B)Has a below average price-to-earnings ratio.
C)Has an average price-to-earnings ratio.
D)Has the minimum possible price-to-earnings ratio.
E)Has the maximum possible price-to-earnings ratio.

Question 39

If we select one box of cereal at random from this population,what is the probability that it will weigh more than 904 grams?

A)8849
B)3849
C)1151
D)7698
E)2302

Question 40

If the random variable X has a mean of $\mu$
And a standard deviation $\sigma$
,then $( X - \mu ) / \sigma$
Has a mean of ____ and standard deviation of _____.

A) $\mu$ and $\sigma$
B) $\bar { X }$ and s
C)1 and 0
D)0 and 1
E)Cannot be determined without more information.

Question 41

Exceeds 3 minutes?

A)3012
B)6988
C)4346
D)5654
E)0821

Question 42

A normal population has a mean of 10 and a variance of 4.What is P(X > 7)?

A)0.6844
B)0.9987
C)0.8913
D)0.7750
E)0.9332

Question 43

What percentage of the time will the number of boxes received weekly be less than 160?

A)0844
B)0987
C)0913
D)0750
E)0228

Question 44

Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25.Using this information,what percentage of the population scores greater than 15?

A)53.28%
B)59.87%
C)49.13%
D)50.00%
E)40.00%

Question 45

What percentage of the time will the number of boxes received weekly be between 180 and 210?

A)5328
B)5987
C)4913
D)7750
E)5332

Question 46

What percentage of the time will the number of boxes received weekly be greater than 210 or less than 180?

A)5328
B)5987
C)4913
D)4672
E)5332

Question 47

A normal population has a mean of 10 and a variance of 4.What is P(X < 6)?

A)0.0228
B)0.4772
C)0.0398
D)0.0438
E)0.4948

Question 48

A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20.What is the number of patrons,x,where 80% are less than x?

A)216.8
B)597.2
C)413.3
D)297.2
E)332.8

Question 49

The distance between store outlets in a chain of stores in a large metropolitan city is normally distributed with an average of 50km and a standard deviation of 5km.What is the probability of finding a store no less than 55km away?

A)0.1668
B)0.2443
C)0.1254
D)0.8727
E)0.1587

Question 50

Is between 2 and 4 minutes?

A)2488
B)4493
C)2019
D)2474
E)1170

Question 51

What percentage of the time will the number of boxes received weekly be greater than 200?

A)6844
B)5000
C)8913
D)7500
E)6332

Question 52

Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25.Using this information,what percentage of the population scores between 10 and 20?

A)53.28%
B)59.87%
C)49.13%
D)50.00%
E)68.26%

Question 53

The distance between store outlets in a chain of stores in a large metropolitan city is normally distributed with an average of 50km and a standard deviation of 5km.What is the probability of finding a store between 50km and 60km?

A)0.2747
B)0.3512
C)0.2997
D)0.4772
E)0.5000

Question 54

The weight of a product is normally distributed with a standard deviation of 0.5 grams.If the production manager wants no more than 5% of the products to weigh more than 5.1 grams,then the average weight should be _____.

A)4.278
B)4.833
C)4.900
D)5.212
E)5.100

Question 55

What percentage of their retired employees would receive payments beyond age 85?

A)13.28%
B)19.87%
C)19.13%
D)10.03%
E)10.90%

Question 56

What percentage of their retired employees would receive payments beyond age 76?

A)53.28%
B)59.87%
C)49.13%
D)46.72%
E)40.90%

Question 57

A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20.What is the number of patrons,x,where 50% are less than x?

A)532
B)597
C)413
D)200
E)332

Question 58

When a ____________ probability distribution is used to approximate a ________ probability distribution we must make a ____________ correction.

A)continuous;discrete;continuity
B)discrete;continuous;continuity
C)continuous;discrete;finite population
D)finite population;world;a global
E)discrete;continuous;finite population

Question 59

Is no more than 3 minutes?

A)3012
B)6988
C)4346
D)5654
E)0821

Question 60

A probability distribution that is useful in describing the time or space between successive occurrences of an event is the _______ probability distribution.

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

Question 61

Given that X is a normal random variable,the probability that a given value of X is below its mean is ________________.

Question 62

A probability distribution that describes the time or space between successive occurrences of an event is a(n)_____ probability distribution.

Question 63

If the random variable of x is normally distributed,____ % of all possible observed values of x will be within two standard deviations of the mean.

Question 64

_____________ values of the standard deviation results in a normal curve that is narrower and more peaked.

Question 65

The standard deviation of a standard normal distribution is always equal to _____.

Question 66

The z-value tells us the number of _____ that a value of x is from the mean.

Question 67

The average distance between store outlets in a chain of stores in a large metropolitan city is 50km and has a standard deviation of 5km. What is the probability of finding a store:

-No less than 55km away?

Question 68

The time of travel from a person's apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.If they leave home at 9:05 AM,what is the probability that they will get to the station between 9:25 and 9:30 AM?

Question 69

If the scores on an aptitude test are normally distributed with mean 500 and standard deviation 100,what proportion of the test scores are less than 585?

Question 70

For a normal population with a mean of 10 and a variance 4,the P(X ≥ 10)is ___.

Question 71

The specific shape of each normal distribution is determined by its _____ and _____.

Question 72

The average distance between store outlets in a chain of stores in a large metropolitan city is 50km and has a standard deviation of 5km. What is the probability of finding a store:



-Between 50 km and 60 km?

Question 73

The mean of a standard normal distribution is always equal to _______.

Question 74

The area under the curve of a valid continuous probability distribution must equal _____.

Question 75

The number of standard deviations that a value x is from the mean is a _____.

Question 76

A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is a(n)_____ distribution.

Question 77

If x is a binomial random variable where n = 100 and p = .1,find the probability that x is less than or equal to 10 using the normal approximation to the binomial.

Question 78

A normal distribution with mean zero and a standard deviation one is called the _____ normal distribution.

Question 79

The thickness of randomly selected metal piece is a ___________ random variable.

Question 80

__________ values of the standard deviation results in a normal curve that is wider and flatter.