Question

The scores for a certain test of intelligence are normally distributed with mean 100 and standard deviation Find the 80th percentile of these scores.

Below is the table used, I still cant figure out what the 80% would be here:

Standard Scores and Percentiles

​z-score

Percentile

​z-score

Percentile

​z-score

Percentile

​z-score

Percentile

minus−3.5

00.02

minus−1.00

15.87

0.00

50.00

1.1

86.43

minus−3.0

00.13

minus−0.95

17.11

0.05

51.99

1.2

88.49

minus−2.9

00.19

minus−0.90

18.41

0.10

53.98

1.3

90.32

minus−2.8

00.26

minus−0.85

19.77

0.15

55.96

1.4

91.92

minus−2.7

00.35

minus−0.80

21.19

0.20

57.93

1.5

93.32

minus−2.6

00.47

minus−0.75

22.66

0.25

59.87

1.6

94.52

minus−2.5

00.62

minus−0.70

24.20

0.30

61.79

1.7

95.54

minus−2.4

00.82

minus−0.65

25.78

0.35

63.68

1.8

96.41

minus−2.3

01.07

minus−0.60

27.43

0.40

65.54

1.9

97.13

minus−2.2

01.39

minus−0.55

29.12

0.45

67.36

2.0

97.72

minus−2.1

01.79

minus−0.50

30.85

0.50

69.15

2.1

98.21

minus−2.0

02.28

minus−0.45

32.64

0.55

70.88

2.2

98.61

minus−1.9

02.87

minus−0.40

34.46

0.60

72.57

2.3

98.93

minus−1.8

03.59

minus−0.35

36.32

0.65

74.22

2.4

99.18

minus−1.7

04.46

minus−0.30

38.21

0.70

75.80

2.5

99.38

minus−1.6

05.48

minus−0.25

40.13

0.75

77.34

2.6

99.53

minus−1.5

06.68

minus−0.20

42.07

0.80

78.81

2.7

99.65

minus−1.4

08.08

minus−0.15

44.04

0.85

80.23

2.8

99.74

minus−1.3

09.68

minus−0.10

46.02

0.90

81.59

2.9

99.81

minus−1.2

11.51

minus−0.05

48.01

0.95

82.89

3.0

99.87

minus−1.1

13.57

minus−0.00

50.00

1.00

84.13

3.5

99.98

Answer 1

given that Mean is 100 and Let s is (x)

For 90th percentile, from z table, the z value is 1.5

thus answer is = mean+s*z=100+x*1.5

=100+1.5(x)

Note:

standard devaition is missing from question.

just place the correct sd value and caluclate for the answer.