Question

1. a patient recently diagnosed with alzheimers disease takes a cognitive abilities test and scores a 45. the mean on this test is 52 and the standard deviation is 5. what is the patients z - score?

a) - 1.4
b) - 1.6
c) 1.4
d) 1.7

1. pat took a spatial abilities test ($\mu=80,\sigma = 8$). pat scored a 76. what is pats z - score?

a) 3
b) 5
c) - 0.5
d) 0.5

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Calculate the z - score for the first problem

For the Alzheimer's disease test, \(x = 45\), \(\mu=52\), \(\sigma = 5\).

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Step3: Calculate the z - score for the second problem

For the spatial abilities test, \(x = 76\), \(\mu = 80\), \(\sigma=8\).

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Answer:

1. a) - 1.4
2. c) - 0.5