ISDS Test PP
A continuous random variable X follows the uniform distribution with a lower limit of A and an upper limit of B. The expected value of X is calculated as ___.
(a+b)/2
Which continuous distributions are positively skewed and bounded below by Zero?
-Lognormal distribution -Exponential distribution.
19.) A joint probability table shows whether a resident has a season pass and if they live on the east or west side of town. What is the probability for a resident with a pass on the east side. (East season pass=0.30), (west season pass=0.45
0.40
If an exponential distribution has the rate parameter λ=5, then the expected value is
1/5
How many parameters are needed to fully describe any normal distribution?
2
If an exponential distribution has an expected value equal to 5, then the standard deviation equals
5
If an exponential distribution has standard deviation equal to 0.20, then the rate parameter λ is
5
22.) Students who take the College Prep English Course the summer before entering college have a 0.84 probability of achieving a "B" or better in their freshman English class at college. The odds that a student taking the Prep Course will receive a "B" or better in the freshman English class are?
5.25 to 1
Which method can be used to help implement the total probability rule?
A probability table
To calculate the probability of the union of two mutually exclusive events A and B.
Add the probability of A to the probability of B
The complement of event A within the sample space S contains
All outcomes in S that are not in A.
The relative frequency of an event is used to calculate what type of probability?
An Empirical probability
The conditional probability of A given B is calculated by dividing the probability of intersection of A and B by the probability of
B
Then updating a prior probability based on new information, which of the following methodologies is MOST useful?
Bayes' Theorem
The shape of the graph depicting the normal probability density function is ___.
Bell shaped
___ is caused by a number of randomly occurring events that are part of the production process.
Chance variation
___ involves dividing a population into mutually exclusive and exhaustive groups, called ___, and then selecting a random sample from these ___ for analysis.
Cluster sampling
A ___ probability is the probability of an event given that another event has already occurred.
Conditional
The total probability rule used to compute an unconditional probability of an event by using
Conditional probabilities
For hotels in NYC, a travel site wants to provide info comparing hotel costs (high, average, low) versus the quality ranking of the hotel (excellent, good, fair, poor). A useful way to summarize these data points is to construct an.
Contingency table
The total area under the normal curve is ___.
Equal to 1
Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event A given event B by the probability of
Event B
The probability distribution of a discrete random variable is called its probability ___
Mass function
The normal distribution is completely described by these two parameters
Mean and Variance
Events that cannot both occur on the same trial of an experiment are ___ ___ events
Mutually exclusive
As a general guideline, the normal distribution approximation can be used to describe the sampling distribution of the sample mean when
N>= 30
We can use the finite population correction factor when
N>= 5%
What is NOT a component of a control chart
Normal curve
The sum of the probabilities of a list of mutually exclusive and exhaustive events is
One
Exponential distribution is based entirely on
One Parameter
If X has a normal distribution with u=100 and o=5, then the probability P(90<x<95) can be expressed in terms of the standard normal random variable Z as
P(-2<Z<-1)
due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to
P(Z<-1.5)
The expected value of (Xbar) is equal to the ___.
Population mean
The expected value of (PBar) is the
Proportion of successes in the population.
When a firm applies statistical techniques to develop and maintain its ability to produce high-quality goods and services, it is implementing statistical ___.
Quality control
Assignable variation is cause by
Specific events that can usually be identified and eliminated.
When a firm inspects the production process to determine at which point the process does not conform to standards, it is applying ___ for statistical quality control
The detection approach.
For a discrete random variable X,
There are countable number of possible values
The exponential random variable is bounded below by ___.
Zero
Probability values range from
Zero to one
The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes
closer to a normal distribution
If x is normally distributed with expected value μ and standard deviation σ, then (Xbar) is normally distributed with
expected value μ and standard deviation σ/(Square Root(n))
For a continuous random variable, one characteristic of its probability density function f(x) is that.
f(x) >= for all values x of X
If the shape of the population from which a simple random is drawn is normal, then the shape of the sampling distribution of (Xbar) is
normal
The High Roller Casino puts the odds of a certain baseball team winning the World Series at (1:30). Based on those odds, what is the probability that this baseball team will in the World Series.
0.032
27.) The probability that an employee earns a promotion is 0.20. The probability that an employee has an MBA is 0.30. The probability that an employee receives a promotion give that the employee has an MBA is 0.25. The probability that an employee has an MBA and gets a promotion is ___.
0.075
Random samples of size 400 are taken from a population whose population proportion is 0.25. The expected value of the sample proportion is
0.25
The probability of randomly selecting a "spade" from a deck of cards is
0.25
Suppose you were told that the delivery time of your new washing machine is equally likely over the time period 9 am to noon. If we define the random variable X as delivery time, then X follows the
Continuous uniform distribution
The probability distribution of a continuous random variable is called its probability ___.
Density function
A particular value of an estimator is called an
Estimate
The poisson random variable counts the number of occurrences of an event over a given interval of time or space while the ___ distribution describes the time that elapses between such occurrences.
Exponential
The probability that a customer will purchase a product is 0.15. The probability that a customer is male is 0.5. the probability that a customer is a male and will purchase a products is 0.075. The events purchasing a product and being male are
Independent
The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter or a test a hypothesis about a parameter is BEST referred to as
Inferential statistics
What does it mean to say that the exponential distribution is "memoryless"?
It has a constant failure rate.
If X is normally distributed with mean = μ and standard deviation = σ, then Y=e^x has which distribution.
Lognormal distribution
what has a failure rate that may increase or decrease over time
Lognormal distribution
What can be said about the expected value and standard deviation of an exponential distribution
The expected value is equal to the standard deviation
What can be represented by a continuous random variable
The high daily temperature in Tampa, Florida during the month of July, measured in degrees.
When some objects are randomly selected, which is most accurate
The order in which objects are selected does not matter in combinations.
What is an Example of a conditional probability
The probability that Lisa purchases groceries, given that Neil has already purchased groceries.
If two events are independent, then the probability that both events occur equals
The product of the individual probabilities.
For a continuous random variable x, how many distinct values can it assume over and interval
Uncountably infinite
A manager of a women's clothing store is projecting next month's sales. Her low-end estimate of sales is $25,000 and her high-end estimate is $50,000. She decides to treat all outcomes for sales between these two values as equally likely. If we define the random variable X as sales, then X follows the
Uniform Distribution
The probability that a discrete random variable X assumes a particular value x is
between zero and one
A firm uses acceptance sampling when
it produces a product and at the end of the process, inspects a portion
A characteristic of normal distribution is that
its symmetric around its mean.
The variance of the standard normal distribution is equal to ___.
one
If X is normally distributed random variable, then
the mean, median, and mode are all equal
Bias can occur in sampling. Bias refers to _______.
the tendency of a sample statistic to systematically over- or under-estimate a population parameter
Selection bias occurs when
there is a systematic exclusion of certain groups from consideration for the sample
Stratified sampling is preferred to cluster sampling when the objective is
to increase precision
In order to convert a contingency table into a joint probability table, the frequency of each cell is divided by the
total number of outcomes in the sample space
Consider data that are normally distributed. In order to transform a standard normal value z into its unstandardized value x, we use the following formula:
x= Mean + (ZSD)
population parameter
μ
18.) The probability that a customer orders popcorn at the movie theater is 0.40. The probability that a customer orders a drink at the movie theater is 0.65. The probability that a customer orders popcorn and a drink is 0.30. If a customer has already ordered popcorn, what is the probability that the customer will order a drink?
0.75
A manufacturing production process is in control if the sample means are
randomly spread out between the control limits
21.) The probability that Margaret earns a Promotion at XYZ corp, is 0.70. The probability that Katia earns a Promotion at ABC inc. is 0.60. If the two promotions are independent, then the probability that both Margaret and Katia earn promotions is ___.
0.42
77.)A population has a mean of 50 and a standard deviation of 10. A random sample of 256 is selected. The standard error is equal to ___
0.625
The probability distribution of the sample mean is commonly referred to as the ___
sampling distribution of (XBar)
For a continuous random variable x, the function used to find the area under f(x) up to any value x is called the
Cumulative distribution function
The z table provides the cumulative probability for a give value z. What does "cumulative probability" mean?
The probability that Z is less than or equal to a given z value
A control chart is a plot of calculated statistics of a production process over ___
Time
26.) A manufacturer of liquid laundry detergent has a 0.02 probability that the detergent bottles will be improperly filled. There is a 0.03 probability that the label on the bottle will not be affixed properly. If the events of bottle fill and affixing the lavel are independent, then the probability that a bottle is filled improperly and has an improperly affixed label is ___.
0.0006
17.) The probability that a patron at Thursday's Restaurant visits the bar area is 0.30. Given that a patron has visited the bar area, the probability of ordering an appetizer is 0.50. The probability of ordering an appetizer, given a patron does not visit the bar area, is 0.20. what is the probability that a patron orders an appetizer?
0.29
Random samples of size 100 are taken from a population whose population proportion is 0.40. The expected value of the sample proportion is ____
0.40
Let P(A)= 0.30 and P(B)= 0.40. Suppose A and B are independent events. Calculate P (A B).
0.40 (since A & B are independent events, P(BIA)=P(B).)
Kareem is trying to decide which college to attend full time next year. Kareem believes there is a 55% chance that he will attend State College and a 33% chance that he will attend North University. The probability that Kareem will attend either State or Northern is
0.88
The variance of (XBAR), which is equal to σ^2/n, is
smaller than the variance σ^2 οφ individual observations