Question

The scores on a test are normally distributed with a mean of 80 and a standard deviation of 16. What isthe score that is 1 1/2 standard deviations above the mean?A score of _ is 1 1/2 standard deviations above the mean.

Answer 1

The formula for z score is given by:

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ \text{ Where} \\ z-is\text{ the z-score} \\ \mu-\text{ is the mean} \\ \sigma-is\text{ the standard deviation} \end{gathered}$$\begin{gathered} \text{ It is given that:} \\ \mu=80 \\ \sigma=16 \\ z=1.5 \end{gathered}$

Therefore,

$\begin{gathered} 1.5=\frac{x-80}{16} \\ \text{ Multiply both sides of the equation by }16 \\ 1.5\times16=\frac{x-80}{16}\times16 \end{gathered}$

Therefore:

$\begin{gathered} 24=x-80 \\ x=80+24 \\ x=104 \end{gathered}$

Therefore, the required score is 104

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