Deck 5: Normal, Binomial, Poisson, and Exponential Distributions

Question 1

A binomial distribution with n number of trials,and probability of success p can be approximated well by a normal distribution with mean np and variance $\sigma ^ { 2 } = n p ( 1 - p ) \text { if } n p > 5 \text { and } n ( 1 - p ) > 5$

Answer 1

True

Question 2

Using the standard normal distribution,the Z-score representing the 5th percentile is 1.645.

Answer 2

False

Question 3

A random variable X is normally distributed with a mean of 175 and a standard deviation of 50.Given that X = 150,its corresponding Z- score is -0.50.

Answer 3

True

Question 4

The binomial distribution is a continuous distribution that is not far behind the normal distribution in order of importance.

Question 5

The Poisson distribution is characterized by a single parameter $\lambda$ ,which must be positive.

Question 6

The binomial random variable represents the number of successes that occur in a specific period of time.

Question 7

For a given probability of success p that is not too close to 0 or 1,the binomial distribution tends to take on more of a symmetric bell shape as the number of trials n increases.

Question 8

The number of loan defaults per month at a bank is Poisson distributed.

Question 9

Much of the study of probabilistic inventory models,queuing models,and reliability models relies heavily on the Poisson and Exponential distributions.

Question 10

The variance of a binomial distribution is given by the formula $\sigma ^ { 2 } = n p ( 1 - p )$
,where n is the number of trials,and p is the probability of success in any trial.

Question 11

The Poisson random variable is a discrete random variable with infinitely many possible values.

Question 12

The binomial distribution is a discrete distribution that deals with a sequence of identical trials,each of which has only two possible outcomes.

Question 13

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time,space,or distance is very small.

Question 14

A random variable X is standardized when each value of X has the mean of X subtracted from it,and the difference is divided by the standard deviation of X.

Question 15

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Question 16

Using the standard normal distribution,the Z- score representing the 99th percentile is 2.326.

Question 17

Using the standard normal curve,the Z- score representing the 75th percentile is 0.674.

Question 18

The binomial distribution deals with consecutive trials,each of which has two possible outcomes.

Question 19

If the random variable X is normally distributed with mean $\mu$ and standard deviation $\sigma$ ,then the random variable Z defined by $Z = ( X - \mu ) / \sigma$ is also normally distributed with mean 0 and standard deviation 1.

Question 20

The Poisson probability distribution is one of the most commonly used continuous probability distributions.

Question 21

An exponential distribution with parameter $\lambda$ = 0.2 has mean and standard deviation both equal to 5.

Question 22

Which of the following equations shows the process of standardizing?

A)
$E ( X ) = n p$
B)
$Z = ( X - \mu \mid \sigma )$
C)
$f ( X ) = 1 - \sigma ( \mu )$
D)
$E ( Y ) = \mu$

Question 23

A Poisson distribution is:

A) relevant when we sample from a population with only two types of members.
B) relevant when we perform a series of independent,identical experiments with only two possible outcomes.
C) usually relevant when we are interested in the number of events that occur over a given interval of time
D) the cornerstone of statistical theory
E) All of these choices

Question 24

The variance of a binomial distribution for which n = 100 and p = 0.20 is:

A) 100
B) 80
C) 20
D) 16

Question 25

The standard deviation $\sigma$
Of a probability distribution is a:

A) measure of variability of the distribution
B) measure of central location
C) measure of relative likelihood
D) measure of skewness of the distribution

Question 26

Given that Z is a standard normal variable,the value z for which P(Z $\leq$ Z)= 0.2580 is

A) 0.70
B) 0.758
C) -0.65
D) 0.242

Question 27

If the value of the standard normal random variable Z is positive,then the original score is where in relationship to the mean?

A) equal to the mean
B) to the left of the mean
C) to the right of the mean
D) None of the these choices

Question 28

One reason for standardizing random variables is to measure variables with:

A) different means and standard deviations on a non-standard scale
B) different means and standard deviations on a single scale
C) dissimilar means and standard deviations in like terms
D) similar means and standard deviations on two scales

Question 29

We assume that the outcomes of successive trials in a binomial experiment are:

A) probabilistically independent
B) probabilistically dependent
C) identical from trial to trial
D) random number between 0 and 1

Question 30

The mean and standard deviation of a normally distributed random variable which has been "standardized" are zero and one,respectively.

Question 31

The total area under the normal distribution curve is equal to one.

Question 32

The mean $\mu$
Of a probability distribution is a:

A) measure of variability of the distribution
B) measure of central location
C) measure of relative likelihood
D) measure of skewness of the distribution

Question 33

Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

Question 34

If the random variable X is exponentially distributed with parameter $\lambda$ = 1)5,then P(2 $\leq$ X $\leq$ 4),up to 4 decimal places,is

A) 0.6667
B) 0.0473
C) 0.5000
D) 0.2500

Question 35

Tossing a coin is an example of a (n)

A) binomial distribution
B) normal distribution
C) exponential distribution
D) Poisson distribution

Question 36

The binomial probability distribution is used with

A) a discrete random variable
B) a continuous random variable
C) either a discrete or a continuous random variable,depending on the variance
D) either a discrete or a continuous random variable,depending on the sample size

Question 37

Using the standard normal curve,the Z- score representing the 10th percentile is 1.28.

Question 38

Sampling done without replacement means that

A) only certain members of the population can be sampled
B) each member of the population can be sampled repeatedly
C) each member of the population can be sampled only once
D) each member of the population can be sampled twice

Question 39

A continuous probability distribution is characterized by:

A) a list of possible values
B) counts
C) an array of individual values
D) a continuum of possible values

Question 40

The Poisson and Exponential distributions are commonly used in which of the following applications

A) Inventory models
B) Financial models
C) Failure analysis models
D) All of these options

Question 41

The standard normal distribution has a mean and a standard deviation respectively equal to

A) 0 and 0
B) 1 and 1
C) 1 and 0
D) 0 and 1

Question 42

What is the variance of the time it takes a technician to fix a computer problem?
A continuous random variable X has the probability density function: f(x)= 2
,
0

Question 43

If the mean of an exponential distribution is 2,then the value of the parameter $\lambda$
Is

A) 4
B) 2
C) 1
D) 0.5

Question 44

Calculate the mean,variance,and standard deviation for the entire year (assume 52 weeks in the year).
A recent survey in Michigan revealed that 60% of the vehicles traveling on highways,where speed limits are posted at 70 miles per hour,were exceeding the limit.Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour.Let X denote the number of vehicles that were exceeding the limit.

Question 45

If we plot a continuous probability distribution f(x),the total probability under the curve is

A) -1
B) 0
C) 1
D) 100
Suppose that the number of customers arriving each hour at the only checkout counter at a local convenience store is approximately Poisson distributed with an expected arrival rate of 30 customers per hour.Let X represent the number of customers arriving per hour.The probabilities associated with X are shown below.
P(X < 5)= 0.0000,P(X < 10)= 0.0000,P(X < 15)= 0.0009,
P(X < 20)= 0.0219,P(X < 25)= 0.1572,P(X < 30)= 0.4757
P(X = 30)= 0.0726,P(X = 31)= 0.0703,P(X = 32)= 0.0659,
P(X = 33)= 0.0599,P(X = 34)= 0.0529,P(X = 35)= 0.0453

Question 46

Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10,P(85 11ea936b_b5ad_521a_b28d_990181381f2c_TB13 6_11X $\leq$ 90)is

A) 0.5328
B) 0.3413
C) 0.1915
D) 0.1498

Question 47

The normal distribution is:

A) a discrete distribution with two parameters
B) a binomial distribution with only one parameter
C) a density function of a discrete random variable
D) a continuous distribution with two parameters

Question 48

What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?
A used car salesman in a small town states that,on the average,it takes him 5 days to sell a car.Assume that the probability distribution of the length of time between sales is exponentially distributed.

Question 49

Which of the following might not be appropriately modeled with a normal distribution?

A) The daily low temperature in Anchorage,Alaska
B) The returns on a stock
C) The daily change in inventory at a computer manufacturer
D) The salaries of employees at a large company

Question 50

The Poisson random variable is a:

A) discrete random variable with infinitely many possible values
B) discrete random variable with finite number of possible values
C) continuous random variable with infinitely many possible values
D) continuous random variable with finite number of possible values

Question 51

Which probability distribution applies to the number of events occurring within a specified period of time or space

A) Binomial distribution
B) Poisson distribution
C) Any discrete probability distribution
D) Any continuous probability distribution

Question 52

Given that Z is a standard normal random variable,P(-1.0 $\leq$ Z $\leq$ 1.5)is

A) 0.7745
B) 0.8413
C) 0.0919
D) 0.9332

Question 53

If the random variable X is exponentially distributed with parameter $\lambda$ = 3,then P(X $\geq$ 2),up to 4 decimal places ,is

A) 0.3333
B) 0.5000
C) 0.6667
D) 0.0025

Question 54

If X is a normal random variable with a standard deviation of 10,then 3X has a standard deviation equal to

A) 10
B) 13
C) 30
D) 90

Question 55

The higher the value of the density function f(x),

A) the less likely the value x
B) the more likely the value x
C) the less likely the distribution is normal
D) None of these choices

Question 56

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter?

A) Uniform
B) Normal
C) Exponential
D) Poisson