Deck 6: Probability and the Normal Distribution

Question 1

Which of the following terms can be used interchangeably?

A) proportions and probabilities
B) proportions and percentages
C) probability and percentages
D) All of the above can be used interchangeably.

Answer 1

A

Question 2

Probability is determined by

A) multiplying the number of items of interest by the number of possible outcomes.
B) multiplying the number of possible outcomes by the number of items of interest.
C) dividing the number of items of interest by the number of possible outcomes.
D) dividing the number of possible outcomes by the number of items of interest.

Answer 2

C

Question 3

What is the probability of drawing an ace from a deck of cards?

A) 1/52
B) 2/52
C) 3/52
D) 4/52

Answer 3

D

Question 4

To say that the tails of the normal distribution are asymptotic means that

A) the left and right sides of the distribution are mirror images of each other.
B) the tails never touch the baseline.
C) the area under the curve is equal to one.
D) proportions are smaller in the tails.

Question 5

To convert a percentage into a proportion,

A) divide by 100.
B) multiply by 100.
C) divide the percentage by the probability.
D) divide the probability by the percentage.

Question 6

You open a "fun size" bag of chocolates covered in a hard shell and find that there are 4 green, 6 yellow, 5 red, and 3 brown candies. If you reach in the bag and withdraw a piece of candy, what is the probability that it will be red?

A) 3.6
B) .25
C) .28
D) .50

Question 7

Column A of the Normal Distribution Table

A) identifies particular z-score values.
B) identifies the proportion in the body of the normal curve.
C) identifies the proportion in the tail of the normal curve.
D) identifies the proportion between the mean and a particular z-score value.

Question 8

Column B of the Normal Distribution Table

A) identifies particular z-score values.
B) identifies the proportion in the body of the normal curve.
C) identifies the proportion in the tail of the normal curve.
D) identifies the proportion between the mean and a particular z-score value.

Question 9

Column C of the Normal Distribution Table

A) identifies particular z-score values.
B) identifies the proportion in the body of the normal curve.
C) identifies the proportion in the tail of the normal curve.
D) identifies the proportion between the mean and a particular z-score value.

Question 10

Column D of the Normal Distribution Table

A) identifies particular z-score values.
B) identifies the proportion in the body of the normal curve.
C) identifies the proportion in the tail of the normal curve.
D) identifies the proportion between the mean and a particular z-score value.

Question 11

Which two columns of the Normal Distribution Table, when added together, equal one?

A) A and D
B) B and C
C) C and D
D) B and D

Question 12

What proportion of the normal distribution is associated with z-scores greater than +1.50?

A) .9332
B) .0668
C) .4332
D) .3413

Question 13

What proportion of the normal distribution is associated with z-scores greater than -1.50?

A) .9332
B) .0668
C) .4332
D) .3413

Question 14

What proportion of the normal distribution is associated with z-scores less than -2.50?

A) .0062
B) .9938
C) .4938
D) .0668

Question 15

In a normal distribution, what proportion of the population will score between the mean and a z-score of -1.00?

A) .8413
B) .1587
C) .3413
D) .4386

Question 16

What z-score is associated with the lowest 15% of the normal distribution?

A) +2.97
B) -2.97
C) +1.04
D) -1.04

Question 17

What z-score is associated with the highest 60% of a normal distribution?

A) -.25
B) +.25
C) -2.51
D) +2.51

Question 18

What z-score is associated with the lowest 2.5% of a normal distribution?

A) -.67
B) +.67
C) -1.96
D) +1.96

Question 19

What z-score value separates the lowest 5% of a normal distribution from the highest 95%?

A) -1.65
B) +1.65
C) -2.57
D) +2.57

Question 20

In a normal distribution, what proportion of the population will have a z-score between -.90 and +1.63?

A) .9484
B) .1325
C) .7643
D) .4484

Question 21

In a normal distribution, what proportion of the population will have a z-score between -.23 and -.84?

A) .1095
B) .7085
C) .3905
D) .2085

Question 22

In a normal distribution, what proportion of the population will have a z-score between +1.00 and +2.33?

A) .3515
B) .1488
C) .8314
D) .6298

Question 23

In a normal distribution, what proportion of the population will have a z-score between -1.23 and +1.23?

A) .7198
B) .7814
C) .5000
D) .6297

Question 24

Karina took an assessment on creativity which resulted in a normal distribution curve. 68% of those who took the assessment scored below her. What is Karina's z-score?

A) +1.49
B) -1.49
C) +.47
D) -.47

Question 25

To find the z-score value is associated with the lowest 20% of the normal distribution, first

A) look in column D of the normal distribution table.
B) translate the 20% into a proportion.
C) look in column B of the normal distribution table.
D) look in column A of the normal distribution table.

Question 26

To find the z-score value associated with the lowest 60% of the normal distribution, first translate the 60% into a proportion, then look in _____________ of the normal distribution table before looking for the associated z-score.

A) column A
B) column B
C) column C
D) column D

Question 27

To find the z-score value associated with the highest 35% of the normal distribution, first translate the 35% into a proportion, then look in _____________ of the normal distribution table before looking for the associated z-score.

A) column A
B) column B
C) column C
D) column D

Question 28

The proportion of the normal distribution that is associated with a z-score greater than +2.50 is .0662. What percentage of the population has a z-score value greater than +2.50?

A) 6.62%
B) 66.20%
C) .0662%
D) .6620%

Question 29

For a normal distribution, p(z > +1.78) =

A) .0375
B) .9625
C) .4625
D) .0213

Question 30

For a normal distribution p(z < +2.33) =

A) .3623
B) .9901
C) .0099
D) .4901

Question 31

For a normal distribution, p(z < -1.68) =

A) .9535
B) .0279
C) .0465
D) .4535

Question 32

For a normal distribution, p(z > -3.05) =

A) .4989
B) .6278
C) .0011
D) .9989

Question 33

If we are looking for the probability that a score will fall between 72 and 92, the correct notation would be

A) p(72 < X < 92).
B) p(72 > X < 92).
C) p(72 > X > 92).
D) p(< 72 X < 92).

Question 34

If we are looking for the proportion of the population that scored between two raw scores, we would first have to

A) translate the raw scores into proportions.
B) look for the proportion in column D of the normal distribution table.
C) convert both raw scores into z-scores.
D) look up the proportion associated with both raw scores in column D and add them together.

Question 35

If we are interested in knowing the proportion of the normal distribution that is associated with two scores that are both located on one side of the mean, then we would

A) add the two proportions together.
B) subtract the smaller proportion from the larger one.
C) subtract the larger proportion from the smaller one.
D) multiply the values of the two proportions together.

Question 36

If we are interested in knowing the proportion of the normal distribution that is associated with two scores that are located on both sides of the mean, then we would

A) add the two proportions together.
B) subtract the smaller proportion from the larger one.
C) subtract the larger proportion from the smaller one.
D) multiply the values of the two proportions together.

Question 37

A normally distributed set of scores has a μ = 58 and a σ = 6. What is the probability that a randomly selected score will fall between 55 and 61?

A) .3413
B) .6170
C) .3830
D) .5000

Question 38

A normally distributed set of scores has a μ = 92 and a σ = 10. What is the probability that a randomly selected score will fall between 72 and 82?

A) .8413
B) .8185
C) .3413
D) .1359

Question 39

If we wanted to determine what raw score is associated with a given z-score, we would use the following formula

A) X = μ - z(σ)
B) X = σ + z(μ)
C) X = z + μ(σ)
D) X = μ + z(σ)

Question 40

A normally shaped distribution has a μ = 85 and a σ = 5. What raw score separates the lower 25% from the upper 75% of the distribution?

A) 90
B) 81.65
C) 88.35
D) 105

Question 41

A normally shaped distribution has a μ= 25 and a σ = 3. What raw score separates the upper 13% of the distribution from the lower 87%?

A) 21.61
B) 26.13
C) 28.39
D) 23.87

Question 42

Given a normally shaped distribution with a μ = 80 and a σ = 8, what scores are so extreme that they are achieved by only 2% of the population?

A) 63.52 and 96.48
B) 61.36 and 98.64
C) 55.36 and 104.64
D) 56.96 and 103.04

Question 43

A die (singular of dice) has six sides. What is the probability of rolling a 3?

Question 44

What column of the normal distribution table would identify the proportions associated with the following z-scores?
a. greater than +1.59 Column _________
b. greater than -2.36 Column __________
c. less than -1.78 Column __________
d. less than +.42 Column __________

Question 45

In a normal distribution, what is the probability of obtaining z-scores
a. greater than +2.00
b. greater than -1.00
c. less than -.50
d. less than +3.00

Question 46

For a normal distribution, determine
a. p(z > -.23)
b. p(z > +2.15)
c. p(z < -1.29)
d. p(z < +.58)

Question 47

What z-score value is associated with the lowest 18% of a normal distribution?

Question 48

What z-score value is associated with the highest 66% of a normal distribution?

Question 49

What z-score value is associated with the highest 2.5% of a normal distribution?

Question 50

What z-score value separates the lowest 70% of a normal distribution from the upper 30%?

Question 51

A normally distributed set of scores has a μ = 69 and σ = 6. What is the probability of obtaining a score less than 72?

Question 52

A normally distributed set of scores has a μ = 25 and σ = 4. What percentage of scores can be expected to score higher than 20?

Question 53

In a normal distribution, find the proportion under the curve between the mean and a z-score of
a. +1.00
b. -2.59
c. .42

Question 54

A normally distributed set of scores has a μ = 86 and σ = 8. What proportion of scores will be between
a. 82 and 96?
b. 75 and 80?

Question 55

For a normally distributed set of scores with a μ = 78 and σ = 9, find
a. p(83 < X < 98)
b. P(62 < X < 88)

Question 56

For a normally distributed set of scores with a μ = 30 and σ = 3, what raw score separates the lower 15% of the distribution from the upper 85%?

Question 57

For a normally distributed set of scores with a μ = 47 and σ = 5, what raw score separates the upper 13% of the distribution from the lower 87%?

Question 58

For a normally shaped distribution with a μ = 54 and σ = 6, what raw scores are so extreme that they will be achieved by only 11% of the population?