Question

A normally distributed data set has a mean of 46 and a standard deviation of 4.5. What z-score corresponds to a data value of 55?

Answer 1

$$Z=\frac{X-\mu}\sigma$$where \(X\) is our statistic, \(\mu\) is its mean, and \(\sigma\) is its standard deviation. Here we're given \(X=55,\mu=46,\sigma=4.5\).

Answer 2

You can think of a Z-score as determining how many standard deviations a statistic is away from its expected value (the mean). So here our difference between our mean and the statistic is \(55-46=9\). Since one standard deviation would be a difference of \(4.5\), here our Z-score is \(9/4.5=2\).

Answer 3

I got 2 :D thank you so much i like how you clearly explained the set up and what each variable stood for

Answer 4

No problem; glad I could help!