Question

What is the z-score of a newborn who weighs 4,000 g?.

Answer 1

The z-score of the considered newborn having 4,000 g weight is $\dfrac{4000 - \mu}{\sigma}$

How to get the z scores?

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

$X \sim N(\mu, \sigma)$

(X is following normal distribution with mean $\mu$ and standard deviation  $\sigma$)

then it can be converted to standard normal distribution as

$Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)$

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

$P(Z \leq z) = P(Z < z) )$

Also, know that if we look for Z = z in z tables, the p value we get is

$P(Z \leq z) = \rm p \: value$

For the considered case, the statement in the problem is missing the mean weight of the newborn and standard deviation of the data set of weights of newborn.

Thus, for them, we can consider variables in place of their actual values.

Let we have:

• X = weights of newborns for some considered system (in grams)
• $\mu$ = mean weight of newborns (in grams)
• $\sigma$ = standard deviation of the data set of weights of newborns

Then, the z-score for X = 4000 is

$z = \dfrac{x - \mu}{\sigma} = \dfrac{4000 - \mu}{\sigma}$

Thus, the z-score of the considered newborn having 4,000 g weight is $\dfrac{4000 - \mu}{\sigma}$

Learn more about z-scores here:

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