Question

1. Transform each of the raw scores in the following hypothetical grade distribution into z scores. Find the area in the upper end of the z distribution for the student who got a score of 93.

Grade

89

90

93

67

74

Answer 1

Solution:

For the given data, we have

Mean = 82.6

SD = 11.4149

Z = (X – mean)/SD

Z for X = 89 is given as below:

Z = (89 – 82.6)/11.4149

Z = 0.560670702

Now, we have to find upper tail probability.

P(Z>0.560670702) = 1 – P(Z<0.560670702) = 1 - 0.712488978 = 0.287511022

All remaining values are given in the following table:

No.	Grade	Z	P(Z>z)
1	89	0.560670702	0.28751102
2	90	0.6482755	0.25840339
3	93	0.911089891	0.18112401
4	67	-1.36663484	0.9141301
5	74	-0.75340126	0.77439559