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Statistics > Exam 2 > Flashcards

Exam 2 Flashcards

1
Q

What is a Random Variable

A
  • a numerical variable
  • its numerical values represent the outcomes of an experiment
  • can be discrete or continuous
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2
Q

What is a Finite number or value

A
  • infinite sequence of values such as 0,1,2…
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3
Q

What is a Continuous Random Variable?

A
  • 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.
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4
Q

What is a Discrete Probability Distribution?

A
  • shows the probability associated with each value of the discrete RV.
  • table, graph or formula
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5
Q

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

A

True

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6
Q

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:

A

Has an above average price-to-earnings ratio

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7
Q

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

A

Zero, one

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8
Q

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.

A

99.73

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9
Q

A property of continuous distributions is that

A

Unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero [P(X = x) = 0].

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10
Q

For a continuous distribution, the exact probability of a particular value is zero.

A

True

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11
Q

The number of standard deviations that a value x is from the mean is a(n) __________

A

z score

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12
Q

The actual weight of hamburger patties is an example of a continuous random variable.

A

True

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13
Q

The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

A

True

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14
Q

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.

A

False

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15
Q

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:

A

The fill weight is less than 910 grams.

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16
Q

____________ values of the standard deviation result in a normal curve that is wider and flatter.

A

Larger

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17
Q

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

A

equal to 0.5

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18
Q

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

A

Mean, standard deviation

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19
Q

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

A

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.

20
Q

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:

A

0 and 1

21
Q

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

A

True

22
Q

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

A

True

23
Q

The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that he scored:

A

Below the mean

24
Q

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.

A

False

25
Q

The normal probability distribution is a discrete probability distribution

A

False

26
Q

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

A

Smaller

27
Q

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

A

True

28
Q

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

A

False

29
Q

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.

A

95.44

30
Q

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

A

Equal to 1

31
Q

Values of the standard normal random variable are measured:

A

In the number of standard deviations from the mean.

32
Q

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

Greater than

33
Q

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

A

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.

34
Q

The spread of the sampling distribution of Picture is ____________ the spread of the corresponding population distribution.

A

Smaller than

35
Q

_____ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed

A

Central Limit Theorem

36
Q

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

A

True

37
Q

If the sampled population is normally distributed, then the sampling distribution of Picture will also have a normal distribution, regardless of the sample size

A

True

38
Q

As the sample size ______________ the variation of the sampling distribution of Picture __________.

A

Increases, decreases

39
Q

A_____isasinglevaluecomputedfromsampleinformationusedtoestimateapopulation parameter.

A

Pointestimate

40
Q

A_____isarangeofvalueswithinwhichthepopulationparameterislikelytooccur.

A

.Confidenceinterval

41
Q

Assumingthesamesamplesizeandthesamestandarddeviation,a95%confidenceintervalwillbe _____thana90percentconfidenceinterval(equalto,wider,narrower,can’ttell)

A

wider

42
Q

A_____showsthefractionofasamplethathasaparticularcharacteristic.

A

proportion

43
Q

Fora95percentconfidenceinterval,approximately_____percentofthesimilarlyconstructed intervalswillincludethepopulationparameterbeingestimated.

A

95

44
Q

Toconstructaconfidenceintervalforamean,thez‐distributionisusedonlywhenthepopulation _____isknown.

A

standard deviation

45
Q

Thefinitepopulationcorrectionfactorisusedwhenthesampleismorethan_____percentofthe population.(5,20,50,100)

A

5

46
Q

Tolocatetheappropriatet‐value,whichisnotnecessary?(degreesoffreedom,levelofconfidence, populationmean)

A

population mean

Statistics (2 decks)

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