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

need to adjust the formula.

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
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