Question

Supposeadistributionof500itemshasamean110andastandarddeviationof10.Findthez-scoreoftheitemx=138.

Answer 1

Let's begin by listing out the information given to us:

n = 500, mean = 110, sd = 10, x = 138

`\begin{gathered} z=(DataPoint-Mean)/(StandardDeviation) \\ z=(x-\mu)/(\sigma)=(138-110)/(10)=(28)/(10)=2.8 \\ z=2.8(the\text{ }datapoint\text{ }is\text{ }above\text{ }average) \end{gathered}`