Exam 2

Question 1

What is a Random Variable

Answer 1

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

Question 2

What is a Finite number or value

Answer 2

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

Question 3

What is a Continuous Random Variable?

Answer 3

• 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.

Question 4

What is a Discrete Probability Distribution?

Answer 4

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

Question 5

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

Answer 5

True

Question 6

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:

Answer 6

Has an above average price-to-earnings ratio

Question 7

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

Answer 7

Zero, one

Question 8

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.

Answer 8

99.73

Question 9

A property of continuous distributions is that

Answer 9

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

Question 10

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

Answer 10

True

Question 11

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

Answer 11

z score

Question 12

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

Answer 12

True

Question 13

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

Answer 13

True

Question 14

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.

Answer 14

False

Question 15

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:

Answer 15

The fill weight is less than 910 grams.

Question 16

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

Answer 16

Larger

Question 17

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

Answer 17

equal to 0.5

Question 18

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

Answer 18

Mean, standard deviation

Question 19

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

Answer 19

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.

Question 20

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:

Answer 20

0 and 1

Question 21

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

Answer 21

True

Question 22

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

Answer 22

True

Question 23

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

Answer 23

Below the mean

Question 24

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.

Answer 24

False

Question 25

The normal probability distribution is a discrete probability distribution

Answer 25

False

Question 26

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

Answer 26

Smaller

Question 27

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

Answer 27

True

Question 28

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

Answer 28

False

Question 29

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.

Answer 29

95.44

Question 30

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

Answer 30

Equal to 1

Question 31

Values of the standard normal random variable are measured:

Answer 31

In the number of standard deviations from the mean.

Question 32

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.

Answer 32

Greater than

Question 33

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

Answer 33

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.

Question 34

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

Answer 34

Smaller than

Question 35

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

Answer 35

Central Limit Theorem

Question 36

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

Answer 36

True

Question 37

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

Answer 37

True

Question 38

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

Answer 38

Increases, decreases

Question 39

 A _____ is a single value computed from sample information used to estimate a population  parameter.  

Answer 39

 Point estimate  

Question 40

 A _____ is a range of values within which the population parameter is likely to occur.  

Answer 40

. Confidence interval  

Question 41

 Assuming the same sample size and the same standard deviation, a 95% confidence interval will be  _____ than a 90 percent confidence interval (equal to, wider, narrower, can't tell)  

Answer 41

wider

Question 42

 A _____ shows the fraction of a sample that has a particular characteristic.  

Answer 42

proportion

Question 43

For a 95 percent confidence interval, approximately _____ percent of the similarly constructed  intervals will include the population parameter being estimated.  

Answer 43

95

Question 44

To construct a confidence interval for a mean, the z‐distribution is used only when the population  _____ is known.  

Answer 44

standard deviation

Question 45

The finite population correction factor is used when the sample is more than _____ percent of the  population. (5, 20, 50, 100)  

Answer 45

5

Question 46

 To locate the appropriate t‐value, which is not necessary? (degrees of freedom, level of confidence,  population mean)  

Answer 46

population mean