Question

1. a graduate school grades with the following system based on z - scores. if a class of 10 students takes a quiz and half get a 90 and half get a 92, the mean is 91 and the standard deviation is 1.05. what are their letter grades using this system?

1. do you like or dislike this system? explain!

Explanation:

Step1: Calculate z - score for 90

The formula for z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For \(x = 90\), \(\mu=91\), \(\sigma = 1.05\)
\(z=\frac{90 - 91}{1.05}=\frac{- 1}{1.05}\approx - 0.95\)

Step2: Calculate z - score for 92

For \(x = 92\), \(\mu = 91\), \(\sigma=1.05\)
\(z=\frac{92 - 91}{1.05}=\frac{1}{1.05}\approx0.95\)

Step3: Determine letter grades

Since \(z\approx - 0.95<1\) for \(x = 90\) and \(z\approx0.95<1\) for \(x = 92\)

Answer:

All students get a letter grade of C.