Question

the class mean for a recent chemistry exam was 85.5 with a standard deviation of 2.2. what is the z---score of a student who receives an 87 on this exam? explain what the z---score represents in regards to class scores.

Answer 1

Mean = 85.5

Standard deviation = 2.2

For a raw score of 87, the z-score is calculated below:

$\begin{gathered} z-\text{score}=\frac{X-\mu}{\sigma} \\ =\frac{87-85.5}{2.2} \\ =\frac{1.5}{2.2} \\ =0.6818 \end{gathered}$

The p-value from z-Table are as follows:

P(x<87) = 0.75232

P(x>87) = 1 - P(x<87) = 0.24768

P(85.5

Therefore:

0. The probability that a student scores less than 87=75.2%

,

1. The probability that a student scores greater than 87=24.8%