Question

Compute z-score. Given ~ n(12,2.5),find z score when x =17

Answer 1

Answer:

The desired z-score is 2.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n(12,2.5)

This means that $\mu = 12, \sigma = 2.5$

z score when x =17

This is Z when X = 17. So

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

$Z = \frac{17 - 12}{2.5}$

$Z = 2$

The desired z-score is 2.