Question

Find the z-scores for the two normally distributed random variables, measured using different units of length.

a) x = 22 in, where X comes from N (15, 2.5)
b) y = 55.88 cm, where Y comes from N (38.1, 6.35)

Answer 1

Using the normal distribution, the z-scores are given as follows:

a) Z = 2.8.

b) Z = 2.8.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

Item a:

The parameters are:

$\mu = 15, \sigma = 2.5$

Hence the z-score is:

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

$Z = \frac{22 - 15}{2.5}$

Z = 2.8.

Item b:

The parameters are:

$\mu = 38.1, \sigma = 6.35$

Hence the z-score is:

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

$Z = \frac{55.88 - 38.1}{6.35}$

Z = 2.8.

More can be learned about the normal distribution at https://brainly.com/question/15181104

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