Question

the scores on a test are normally distributed with a mean of 80 and a standard deviation of 16. what is the score that is $\frac{1}{2}$ standard deviation above the mean? a score of is $\frac{1}{2}$ standard deviation above the mean.

Explanation:

Step1: Identify given values

Mean $\mu = 80$, Standard - deviation $\sigma=16$.

Step2: Calculate the score

The score $x$ that is $\frac{1}{2}$ standard deviation above the mean is given by the formula $x=\mu+\frac{1}{2}\sigma$. Substitute $\mu = 80$ and $\sigma = 16$ into the formula: $x = 80+\frac{1}{2}\times16$.

Step3: Simplify the expression

First, calculate $\frac{1}{2}\times16 = 8$. Then, $x=80 + 8=88$.

Answer:

88