Exam 2 Flashcards Preview

Statistics > Exam 2 > Flashcards

Flashcards in Exam 2 Deck (46)
Loading flashcards...
1

What is a Random Variable

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

2

What is a Finite number or value

- infinite sequence of values such as 0,1,2...

3

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.

4

What is a Discrete Probability Distribution?

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

5


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

True

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:

Has an above average price-to-earnings ratio

7

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


Zero, one

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.


99.73

9

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].

10

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

True

11

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



z score

12

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

True

13

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

True

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.

False

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:


The fill weight is less than 910 grams.

16

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

Larger

17

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

18

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


Mean, standard deviation

19

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.

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:

0 and 1

21

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

True

22

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

True

23

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

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.

False

25

The normal probability distribution is a discrete probability distribution

False

26

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

Smaller

27

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

True

28

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

False

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.

95.44

30

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

Equal to 1

31

Values of the standard normal random variable are measured:



In the number of standard deviations from the mean.

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.


Greater than

33

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.

34

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

Smaller than

35

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

Central Limit Theorem

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

True

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

True

38

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

Increases, decreases

39

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

 Point estimate  

40

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

. Confidence interval  

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)  

wider

42

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

proportion

43

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

95

44

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

standard deviation

45

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

5

46

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

population mean