3.2 Probability with the Standard Normal Distribution

[defn] What is the mean (µ) and standard deviation (σ) of the standard normal distribution (z-distribution)?

a) Mean = 0, and standard deviation = 1.

b) Mean = 1, and standard deviation = 0.

c) Mean = any value, and standard deviation = 1.

d) Mean = any fixed value, and standard deviation = any varying value.

a

[defn] There are an infinite number of standard normal distributions.

t/f

f

[defn] The standard normal distribution ( z-distribution) follows the Empirical Rule of statistics.

t/f

t

[defn] The area under the standard normal curve = 1.

t/f

t

[defn] The z-curve is a graph of what distribution?

a) The standard normal distribution.

b) Any normal distribution.

c) Any bell shaped distribution.

d) The distribution of frequencies of the data values.

a

[defn] In the standard normal distribution, what are z-scores used to describe?

a) The area under the curve.

b) The area over the event and under the curve.

c) Both areas and events.

d) The event on the x-axis.

d

[defn] What is the range of z-scores?

a) 0 < 𝓏 < 1

b) –∞ < 𝓏 < +∞

c) 0 < 𝓏 < +∞

d) -3 < 𝓏 < +3

b

[calc] Match the appropriate tail area for each of the z-scores below.

A.  -0.97

B.  -2.85 

C.  +1.97

-0.0244

-0.0022

-0.1660

[calc] Match the appropriate body area for each of the  z-scores below.

A.  Left body area from  z = +1.97.

B.  Right body area from  z = -2.85.

C.  Right body area from  z = -0.97. 

-0.9756

-0.9978

-0.8340

a, b, c

[calc] Match the magnitude of the appropriate z-score to each of the tail areas below.

A.  0.1814

B.  0.0256 

C.  0.0036

-2.69

-0.91

-1.95

c, a, b

[calc] Match the magnitude of the appropriate z-score to each of the body areas below.

A.  A right body area = 0.9960.

B.  A left body area = 0.7995. 

C.  A left body area = 0.9599. 

-1.75

- -2.65

- 0.84

c, a, b

[calc] Use the schematic curve and the z-table to find the probability of an individual having a z-score greater than +2.00?

a) 0.0228

b) 0.9772

c) 0.0235

d) 0.0500

a

[calc] Use the schematic curve and the z-table to find the proportion of a population between z = -2.33 and z = +2.33?

a) 0.0099

b) 0.9901

c) 0.8389

d) 0.9802

d

[calc] Use the schematic curve and the z-table to find the probability of an individual having a z-score greater than -1.55?

a) 0.0606

b) 0.1212

c) 0.9394

d) 0.8788

c

[calc] Use the schematic curve and the z-table to find the proportion of a population having a z-score less than +0.44?

a) 0.6700

b) 0.3300

c) 0.5600

d) 0.1500

a

[calc] Use the schematic curve and the z-table to find the proportion of a population between z = -1.96 and z = +1.96?

a) 0.9750

b) 0.9500

c) 0.0250

d) 1.0500

b

[calc] Use the schematic curve and the z-table to find the proportion of a population between z = +1.77 and z = +1.96?

a) 0.0134

b) 0.0384

c) 0.0250

d) 0.0634

a

[calc] Use the schematic curve and the z-table to find the proportion of a population between z = -1.40 and z = +2.40?

a) 0.9192

b) 0.0890

c) 0.0726

d) 0.9110

d

[calc] Use the schematic curve and the z-table to find the proportion of a population less than z = -1.96 and greater than z = +1.96?

a) All of the other answers.

b) 0.0500

c) Two times the area in one tail.

d) This is a two-tail situation so the area of interest = 0.0250 + 0.0250.

a

[calc] Use the schematic curve and the z-table to find the probability of an individual in a population following the standard normal curve being less than (or greater than) the mean?

a) The mean and standard deviation are needed for this calculation.

b) A z-score is needed for this calculation.

c) 0.5000

d) None of the other answers.

c

[calc] Use the schematic curve and the z-table to find the z-score that bounds the top 2.02% of a population.

a) +2.02

b) -2.02

c) +2.05

d) +0.9798

c

[calc] Use the schematic curve and the z-table to find the z-score that bounds the top 79.95% of a population.

a) -0.84

b) -0.53

c) +0.21

d) -0.21

a

[calc] Use the schematic curve and the z-table to find the z-scores that bound the middle 79.95% of a population.

a) -0.84, +0.84

b) -1.28, +1.28

c) -0.25, +0.25

d) -0.21, +0.21

b

[calc] For a side area in the schematic curve, how many lines are drawn and on which side of the curve are they drawn?

a) Two lines on the same side.

b) Two lines on opposite sides.

c) One line in the middle and one line on one side. 

d) Two lines in the same place.

a

[calc] Use the schematic curve and the z-table to find the z-score that separates the bottom 86% of the individuals from the top 14% ?

a) z = +0.44

b) z = -1.08

c) z = -0.44

d) z = +1.08

d

[calc] Use the schematic curve and the z-table to find what z-score separates the bottom 5% of the individuals from the top 95% ?

a) z = +0.95

b) z = -0.48

c) z = -1.64

d) z = -2.58

c

[calc] Use the schematic curve and the z-table to find what are the z-scores for the first quartile (Q₁), and for the third quartile (Q₃).

a) (Q₁) is at z = -0.67, and (Q₃)   is at z = +0.67 .

b) (Q₁) is at z = -1.96, and (Q₃) is at z = +1.96 .

c) (Q₁) is at z = -2.81, and (Q₃) is at z = +2.81 .

d) (Q₁) is at z = 0.25, and (Q₃) is at z = 0.75 .

a

[calc] What is the range of  z-scores for the middle 82% of a population that follows the standard normal curve?

a) Range of  z-scores = (-1.28, +1.28) .

b) Range of  z-scores = (-1.34, +1.34) .

c) Range of  z-scores = (+1.28, -1.28) .

d) Range of  z-scores = (-1.96, +1.96) .

b