Question

For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.

Answer 1

The z-score is
`z = 0.6`

The percentile is
`p(Z < 0.6) = 72.57\%`

Explanation:

From the question we are told that

The data value is 0.6 standard deviations above the mean i.e
`x = \mu + 0.6 \sigma`

Where
`\mu` is the population mean and
`\sigma` is the standard deviation

Generally the z-score is mathematically represented as

`z = (x - \mu )/(\sigma )`

=>
`z = ((\mu + 0.6\sigma ) - \mu )/(\sigma )`

=>
`z = 0.6`

The percentile is obtained from the z-table and the value is

`p(Z < 0.6) = 0.7257`

=>
`p(Z < 0.6) = 72.57\%`