Question

Use the accompanying table of standard scores and their percentiles under the normal distribution to find the approximate standard score of the following data values. Then state the approximate number of standard deviations that the value lies above or below the mean.

a. A data value in the 80th percentile

b. A data value in the 60th percentile

c. A data value in the 92nd percentile

a. The standard score for the 80th percentile is approximately

nothing.

​(Round to two decimal places as​ needed.)

​(Round to two decimal places as​ needed.)

z-score Percentile

-3.5        0.02

-3.0        0.13

-2.9        0.19

-2.8        0.26

-2.7        0.35

-2.6        0.47

-2.5        0.62

-2.4        0.82

-2.3        1.07

-2.2        1.39

-2.1        1.79

-2.0        2.28

-1.9        2.87

-1.8        3.59

-1.7        4.46

-1.6        5.48

-1.5        6.68

-1.4        8.08

-1.3        9.68

-1.2        11.51

-1.1        13.57

-1.0        15.87

-0.95      17.11

-0.90      18.41

-0.85      19.77

-0.80      21.19

-0.75      22.66

-0.70      24.2

-0.65      25.78

-0.60      27.43

-0.55      29.12

-0.50      30.85

-0.45      32.64

-0.40      34.46

-0.35      36.32

-0.30      38.21

-0.25      40.13

-0.20      42.07

-0.15      44.04

-0.10      46.02

-0.05      48.01

0.0          50.0

0.05        51.99

0.1          53.98

0.15        55.96

0.2          57.93

0.25        59.87

0.3          61.79

0.35        63.68

0.4          65.54

0.45        67.36

0.5          69.15

0.55        70.88

0.6          72.57

0.65        74.22

0.7          75.8

0.75        77.34

0.8          78.81

0.85        80.23

0.9          81.59

0.95        82.89

1.0          84.13

1.1          86.43

1.2          88.49

1.3          90.32

1.4          91.92

1.5          93.32

1.6          94.52

1.7          95.54

1.8          96.41

1.9          97.13

2.0          97.72

2.1          98.21

2.2          98.61

2.3          98.93

2.4          99.18

2.5          99.38

2.6          99.53

2.7          99.65

2.8          99.74

2.9          99.81

3.0          99.87

3.5

Answer 1

Solution:

a)

From the information, observe that the table of standard scores and their percentiles under the normal distribution.

The data value in the 80^th percentile.

From the standard normal table values, observe that the standard score for the corresponding to the 80^th percentile is 0.85

Therefore, the 80^th percentile lies approximately 0.85 standard deviations below the mean.

b)

From the information, observe that the table of standard scores and their percentiles under the normal distribution.

The data value in the 60^th percentile.

From the standard normal table values, observe that the standard score for the corresponding to the 60^th percentile is 0.25

Therefore, the 60^th percentile lies approximately 0.25 standard deviations below the mean.

c)

From the information, observe that the table of standard scores and their percentiles under the normal distribution.

The data value in the 92^nd percentile.

From the standard normal table values, observe that the standard score for the corresponding to the 92^ndpercentile is 0.33

Therefore, the 63^rd percentile lies approximately 1.4 standard deviations above the mean.