Deck 6: Standard Scores and the Normal Curve

Question 1

In a normal distribution, what proportion of cases fall between:
(a)z = -1.00 and
(b)

and

(c)

and

(d)
and

(e)
and

Answer 1

(a).6826
(b).9544
(c).6678
(d).1210
(e).2853.

Question 2

The gasoline mileages for city driving obtained by drivers of a certain brand of compact car are normally distributed with

m.p.g. and S_X = 2.3 m.p.g. What proportion of drivers obtain:
(a)less than 23 m.p.g.?
(b)less than 30 m.p.g.?
(c)between 25 and 30 m.p.g.?
(d)between 28 and 32 m.p.g.?

Answer 2

(a).0375
(b).8962
(c).7148
(d).3317.

Question 3

A well-known IQ test is standardized to have a mean of 100 and a standard deviation of 15 for children of any particular age level. Out of a typical sample of 500 children of a given age, how many would we expect to obtain IQ scores:
(a)above 130?
(b)above 150?
(c)below 80?
(d)between 90 and 110?
(e)outside the limits 80 and 120?

Answer 3

(a)11
(b)less than 1 (.25)
(c)46
(d)249
(e)92.

Question 4

The frequency distribution of lifetimes of a tiny battery to power hand calculators is normal with

and

. Out of every 1000 batteries produced, how many would we expect to last:
(a)over 600 hours?
(b)less than 550 hours?
(c)between 500 and 550 hours?
(d)between 550 and 600 hours?
(e)over 650 hours?

Question 5

In a normal distribution of employment screening test scores with a mean of 95 and a standard deviation of 25, what is (are) the score(s):
(a) above which the top 5% of the cases fall?
(b) below which the bottom 52% of the cases fall?
(c) below which the bottom 88% of the cases fall?
(d) below which the bottom 10% of the cases fall?
(e) between which the central 30% of the cases lie?

Question 6

For a sample of 200 laboratory rats, the mean time to traverse a special experimental maze on the first trial was 22.5 seconds with a standard deviation of 4.7 seconds. Use the normal curve model to estimate the value(s):
(a)below which the 20 shortest time scores fell;
(b)above which the 50 longest time scores fell;
(c)below which the 130 shortest time scores fell;
(d)between which the central 140 time scores fell

Question 7

Four-thousand entering freshmen at Downtown University take a mathematics proficiency test. The mean of the test is 60 with a standard deviation of 10; scores are normally distributed.
(a) The university has decided to place students who earned a score of 72 or better into honors math. How many students will be placed in honors math?
(b) The university has decided to place the bottom 30% into remedial math. What score must be earned to avoid being placed into remedial math?
(c) How many students earned a score between 45 and 55?

Question 8

The normal curve is

A) a mathematical abstraction having a particular defining equation
B) a law of nature
C) both (a) and (b)
D) none of the above

Question 9

All normal curves

A) are unimodal
B) are symmetrical
C) are asymptotic to the horizontal axis
D) have all of the above properties

Question 10

Which, if any, is not a property of the normal curve?

A) it is continuous
B) its mean and median differ only slightly
C) its mean may take various values
D) its standard deviation may take various values

Question 11

Which of the following characteristics is the same for all normal curves?

A) their means
B) their standard deviations
C) their slope
D) all of the above

Question 12

The proportion of cases in a normal distribution falling between
and

is approximately

A) .25
B) .50
C) .67
D) 1.34

Question 13

In a normal distribution, what proportion of cases falls below

A) .4192
B) .0808
C) .9192
D) .5808

Question 14

In a normal distribution of 200 cases, how many fall between
and

A) 173
B) 87
C) 43
D) 27

Question 15

In a normal distribution of 200 cases, how many fall above

A) 39
B) 79
C) 21
D) 11

Question 16

In a normal distribution with
and S_X = 10, what proportion of cases fall above a score of 42?

A) .7881
B) .2119
C) .2881
D) .7119

Question 17

In a normal distribution with
and S_X = 10, what proportion of cases fall between 45 and 55?

A) .3085
B) .3830
C) .6170
D) .1915

Question 18

In a normal distribution of scores with
and S_X = 10, what proportion of cases fall above a score of 62?

A) .7698
B) .3849
C) .1151
D) .0478

Question 19

In a normal distribution of 400 scores with
and S_X = 10, how many fall below 35?

A) 71
B) 27
C) 37
D) 47

Question 20

In a normal distribution of 400 scores with
and S_X = 10, how many cases fall between 50 and 60?

A) 98
B) 142
C) 68
D) 137

Question 21

In a normal distribution, the bottom 75% of the cases fall below what z score?

A) +.50
B) +.38
C) +1.28
D) +.67

Question 22

In a normal distribution of 200 cases, the bottom 40 cases fall below what z score?

A) -.25
B) -.84
C) -.52
D) -.37

Question 23

In a normal distribution of 200 cases, what z score divides the top 20 cases from the bottom 180?

A) +1.28
B) +.25
C) +.84
D) +1.96

Question 24

In a normal distribution the most extreme 5% of the cases fall beyond z =

A) -1.64
B) -2.58
C) -1.96
D) -1.80

Question 25

In a normal distribution, the middle 20% of the cases fall between what two z scores?

A) -.52 and +.52
B) -.84 and +.84
C) -1.28 and +1.28
D) -.25 and +.25

Question 26

In a normal distribution with
and S_X = 10, the bottom 80% of the cases fall below what score (rounded)?

A) 63
B) 54
C) 61
D) 58

Question 27

In a normal distribution with
and S_X = 10, the middle 50% of the cases fall between what scores (rounded)?

A) 41 and 59
B) 43 and 57
C) 38 and 62
D) 45 and 55