Question

Suppose the random variable x is best described by a normal distribution with μ=23 and σ=4. Find the z-score that corresponds to each of the following x values.

(a) x=32
z=

(b) x=29
z=

(c) x=16
z=

(d) x=36
z=

(e) x=14
z=

(f) x=37
z=

Answer 1

Answer:

a) $Z = 2.25$

b) $Z = 1.50$

c) $Z = -1.75$

d) $Z = 3.25$

e) $Z = -2.25$

f) $Z = 3.50$

Step-by-step explanation:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

In this problem, we have that:

$\mu = 23, \sigma = 4$

(a) x=32

z=

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{32 - 23}{4}$

$Z = 2.25$

(b) x=29

z=

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{29 - 23}{4}$

$Z = 1.50$

(c) x=16

z=

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16 - 23}{4}$

$Z = -1.75$

(d) x=36

z=

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{36 - 23}{4}$

$Z = 3.25$

(e) x=14

z=

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{14 - 23}{4}$

$Z = -2.25$

(f) x=37

z=

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{37 - 23}{4}$

$Z = 3.50$