Question

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

Answer 1

The desired z-score is 2.

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 = (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 = (X - \mu)/(\sigma)`

`Z = (17 - 12)/(2.5)`

`Z = 2`

The desired z-score is 2.