Exam 2 Flashcards
What is a Random Variable
- a numerical variable
- its numerical values represent the outcomes of an experiment
- can be discrete or continuous
What is a Finite number or value
- infinite sequence of values such as 0,1,2…
What is a Continuous Random Variable?
- any numerical value in one or more intervals.
ex. waiting time at a teller window, interest rate on a loan - continuous means that the number of possible real numbers in any interval is infinite.
- often referred to as probability density functions.
What is a Discrete Probability Distribution?
- shows the probability associated with each value of the discrete RV.
- table, graph or formula
The z value tells us the number of standard deviations that a value x is from the mean.
True
The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution. In this industry, a firm with a standard normal variable value of z = 1:
Has an above average price-to-earnings ratio
A standard normal distribution has a mean of ____________ and standard deviation of ____________.
Zero, one
If the random variable x is normally distributed, ______ percent of all possible observed values of x will be within three standard deviations of the mean.
99.73
A property of continuous distributions is that
Unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero [P(X = x) = 0].
For a continuous distribution, the exact probability of a particular value is zero.
True
The number of standard deviations that a value x is from the mean is a(n) __________
z score
The actual weight of hamburger patties is an example of a continuous random variable.
True
The number of defective pencils in a lot of 1000 is an example of a continuous random variable.
True
In a statistical study, the random variable X = 1 if the house is colonial, and X = 0 if the house is not colonial. The random variable X is continuous.
False
The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. 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:
The fill weight is less than 910 grams.
____________ values of the standard deviation result in a normal curve that is wider and flatter.
Larger
Given that X is a normal random variable, the probability that a given value of X is below its mean is ________________.
equal to 0.5
The specific shape of each normal distribution is determined by its ____________ and ____________.
Mean, standard deviation
The relationship between the standard normal random variable z and normal random variable X is that:
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.
If the random variable X has a mean of µ and a standard deviation σ, then (X - µ)/σ has a mean and standard deviation respectively:
0 and 1
The standard deviation of a standard normal distribution is always equal to 1.
True
The mean and median are the same for a normal distribution.
True
The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that he scored:
Below the mean
If the random variable x is normally distributed, 68.26 percent of all possible observed values of x will be within two standard deviations of the mean.
False
The normal probability distribution is a discrete probability distribution
False
____________ values of the standard deviation result in a normal curve that is narrower and more peaked.
Smaller
For a continuous distribution, P(X ≤ 100) = P(X
True
The mean of a standard normal distribution is always equal to 1.
False
If the random variable of x is normally distributed, _____ percent of all possible observed values of x will be within two standard deviations of the mean.
95.44
The area under the curve of a valid continuous probability distribution must ____________.
Equal to 1
Values of the standard normal random variable are measured:
In the number of standard deviations from the mean.
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.
Greater than
Which of the following statements is not a property of the normal probability distribution?
95.44 percent of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean.
The spread of the sampling distribution of Picture is ____________ the spread of the corresponding population distribution.
Smaller than
_____ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed
Central Limit Theorem
If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of Picture with a normal distribution
True
If the sampled population is normally distributed, then the sampling distribution of Picture will also have a normal distribution, regardless of the sample size
True
As the sample size ______________ the variation of the sampling distribution of Picture __________.
Increases, decreases
A_____isasinglevaluecomputedfromsampleinformationusedtoestimateapopulation parameter.
Pointestimate
A_____isarangeofvalueswithinwhichthepopulationparameterislikelytooccur.
.Confidenceinterval
Assumingthesamesamplesizeandthesamestandarddeviation,a95%confidenceintervalwillbe _____thana90percentconfidenceinterval(equalto,wider,narrower,can’ttell)
wider
A_____showsthefractionofasamplethathasaparticularcharacteristic.
proportion
Fora95percentconfidenceinterval,approximately_____percentofthesimilarlyconstructed intervalswillincludethepopulationparameterbeingestimated.
95
Toconstructaconfidenceintervalforamean,thez‐distributionisusedonlywhenthepopulation _____isknown.
standard deviation
Thefinitepopulationcorrectionfactorisusedwhenthesampleismorethan_____percentofthe population.(5,20,50,100)
5
Tolocatetheappropriatet‐value,whichisnotnecessary?(degreesoffreedom,levelofconfidence, populationmean)
population mean
