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Answer the question correctly I will provide the docs that you need to answer the question. Make sure you use the chart correctly to answer the questionStandardized Score In-Class Examples
1. Calculate the z-score for the following raw scores given a mean of 13.2 and a standard
deviation of 2. After you have calculated that, please calculate the percent of score that
fall below that given z-score.
Raw
Z-score Percent below
13.2
15.2
16.8
11.6
2. Calculate the z-score for the following raw scores given a mean of 13.2 and a standard
deviation of 2. After you have calculated that, please calculate the percent of score that
fall below that given z-score. However, a lower score is better in this instance, so you will
Raw
13.2
15.2
16.8
11.6
Z-score
Percent below
3. What percentage of data fall between a z-score of -1 and 1?
4. What percentage of data fall between a z score of -2.3 and 1?
5. What percentage of that data fall below a z-score of -2 and above 2?
6. What z-scores would 92% of the data fall between?
7. You are asked to develop a normative table for a newly developed test of aerobic
fitness. Briefly, people run for 15 minutes and their total mileage is recorded as their
score. The thought is the higher the mileage, the higher the aerobic fitness. You tested a
huge population of individuals and found the mean mileage to be 1.6 miles with a
standard deviation of 0.26. Fill in the raw scores in the table below that corresponds to
the percentile.
Percentile
95th
75th
50th
25th
5th
Raw Score
8. A country town installs 2000 new electric lights in a new housing estate. These lamps
have an average life of 1000 hours with a standard deviation of 200 hours. Hint: Draw
and label a normal “bell-shaped” curve to help answer this
a) What percentage of bulbs would be expected to fail between 800 hours and 1200
hours?
b) How many bulbs would this be?
c) How many bulbs would be expected to last longer than 1600 hours?
Chapter 3
Danilo Tolusso, PhD
EXS 324– Measurement and Evaluation in Kinesiology

Percentile Rank
▪ A relative position (out of 100) that
indicates the percentage of total
scores that ____________a certain
number
▪ Highest score ranks 1, second
highest ranks 2….

Percentile
▪ This is a ____________that
corresponds to a percentile rank
Position
VO2max
(Percentile)
Percentile
Rank
1
68.9
100
2
66.4
90
3
62.8
80
4
51.2
70
5
46.7
60
6
42.4
50
7
41.0
40
8
39.0
30
9
38.8
20
10
37.2
10
Score
(Percentile)
Frequency
Cumulative
Frequency
Percentile Rank
40
38
36
35
32
30
28
26
24
22
1
2
2
3
4
4
3
2
1
1
23
22
20
18
15
11
7
4
2
1
23/23=100
22/23=96
18/23=78
15/23=65
7/23=30
2/23=9
1/23=4

The empirical rule states that in a normal
distribution…
▪ ___% of the data will between -1 and +1 SD from
the mean
▪ ___% of the data will between -2 and +2 SD from
the mean
▪ ____ % of the data will between -1 and +1 SD
from the mean
▪ Link for a more visual description
Competition Activity
Nick Saban
Bear Bryant
Bench Press (lbs)
1
-2
100 Meter Sprint (seconds)
1
3
Standing Long Jump (feet)
1
2
Bench Percentile:
100m Percentile:
Long Jump Percentile:

When z-scores are whole numbers then it is easy to calculate the
percent of scores below a given z-score. However, what happens
when z-scores are not integers (whole numbers)?

We use a z-table!
▪ Relates a z-score to a given percentile in a normal distribution
▪ Splits the distribution into left and right

Three types of tables often used that tell us the same information in
different ways
▪ We will be using the cumulative from mean table that is located in your
textbook.
▪ Also included on next page
Z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.00
0.40
0.80
1.20
1.60
1.99
2.39
2.79
3.19
3.59
3.98
4.38
4.78
5.17
5.57
5.96
6.36
6.75
7.14
7.53
7.93
8.32
8.71
9.10
9.48
9.87
10.26
10.64
11.03
11.41
11.79
12.17
12.55
12.93
13.31
13.68
14.06
14.43
14.80
15.17
15.54
15.91
16.28
16.64
17.00
17.36
17.72
18.08
18.44
18.79
19.15
19.50
19.85
20.19
20.54
20.88
21.23
21.57
21.90
22.24
22.57
22.91
23.24
23.57
23.89
24.22
24.54
24.86
25.17
25.49
25.80
26.11
26.42
26.73
27.04
27.34
27.64
27.94
28.23
28.52
28.81
29.10
29.39
29.67
29.95
30.23
30.51
30.78
31.06
31.33
31.59
31.86
32.12
32.38
32.64
32.89
33.15
33.40
33.65
33.89
34.13
34.38
34.61
34.85
35.08
35.31
35.54
35.77
35.99
36.21
36.43
36.65
36.86
37.08
37.29
37.49
37.70
37.90
38.10
38.30
38.49
38.69
38.88
39.07
39.25
39.44
39.62
39.80
39.97
40.15
40.32
40.49
40.66
40.82
40.99
41.15
41.31
41.47
41.62
41.77
41.92
42.07
42.22
42.36
42.51
42.65
42.79
42.92
43.06
43.19
43.32
43.45
43.57
43.70
43.82
43.94
44.06
44.18
44.29
44.41
44.52
44.63
44.74
44.84
44.95
45.05
45.15
45.25
45.35
45.45
45.54
45.64
45.73
45.82
45.91
45.99
46.08
46.16
46.25
46.33
46.41
46.49
46.56
46.64
46.71
46.78
46.86
46.93
46.99
47.06
47.13
47.19
47.26
47.32
47.38
47.44
47.50
47.56
47.61
47.67
47.72
47.78
47.83
47.88
47.93
47.98
48.03
48.08
48.12
48.17
48.21
48.26
48.30
48.34
48.38
48.42
48.46
48.50
48.54
48.57
48.61
48.64
48.68
48.71
48.75
48.78
48.81
48.84
48.87
48.90
48.93
48.96
48.98
49.01
49.04
49.06
49.09
49.11
49.13
49.16
49.18
49.20
49.22
49.25
49.27
49.29
49.31
49.32
49.34
49.36
49.38
49.40
49.41
49.43
49.45
49.46
49.48
49.49
49.51
49.52
49.53
49.55
49.56
49.57
49.59
49.60
49.61
49.62
49.63
49.64
49.65
49.66
49.67
49.68
49.69
49.70
49.71
49.72
49.73
49.74
49.74
49.75
49.76
49.77
49.77
49.78
49.79
49.79
49.80
49.81
49.81
49.82
49.82
49.83
49.84
49.84
49.85
49.85
49.86
49.86
49.87
49.87
49.87
49.88
49.88
49.89
49.89
49.89
49.90
49.90
1RM Bench Press Example
Raw Score= 275 lb
Mean
= 250
SD
=25
Z
=1
Z(1)
=?
 Positive Z-Score Video
1RM Bench Press Example
Raw Score= 225 lb
Mean
= 250
SD
=25
Z
=-1
Z(-1)
=?
 Negative Z-Score Video
Competition Activity
Nick Saban
Bear Bryant
M ± SD
Bench Press (lbs)
1
-2
200 ± 10
100 Meter Sprint (seconds)
1
3
13 ± 1
Standing Long Jump (feet)
1
2
9±1
Bench Percentile:
100m Percentile:
Long Jump Percentile:
Competition Activity
Nick Saban
Bear Bryant
M ± SD
Bench Press (lbs)
1
-2
200 ± 10
100 Meter Sprint (seconds)
1
3
13 ± 1
Standing Long Jump (feet)
1
2
9±1
Bench Percentile:
100m Percentile:
Long Jump Percentile:

Can be thought of as the probability that a certain number is above or below
a z score

Can also be used to determine probability of a score being between two zscores

P( z ≤ 0)
▪ This is asking, what is the probably that a zscore is less than 0

P(-1.0 < z < 1.0) ▪ This is asking, what is the probably that a zscore is between -1 and 1. P(-2 < z < 2) P(-1.2 < z < 1.0) You are a PT working with an athlete post-surgery. You find a study that that develops a new test for post-operative ACL assessment. The researchers performed a study and found that the 68th percentile was the cut-off percentile rank for allowing your athlete to return to play. This involved looking at the probability of re-injury and determining a cut-off value where they saw a greatly reduced risk of re-injury. The mean and standard deviation for this test was 7.6 ± .81 and your athlete had a score of 8.3. Can he return to play or not? Solution Video Purchase answer to see full attachment

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