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 88 is $\frac{1}{2}$ standard deviation above the mean.

Explanation:

Step1: Identify given values

Mean $\mu = 80$, standard - deviation $\sigma=16$, number of standard deviations $z = 0.5$.

Step2: Use the formula for z - score transformation

The formula for a value $x$ in terms of the mean, standard deviation and z - score is $x=\mu + z\sigma$.
Substitute $\mu = 80$, $z = 0.5$ and $\sigma = 16$ into the formula: $x=80+0.5\times16$.

Step3: Calculate the value of x

First, calculate $0.5\times16 = 8$. Then, $80 + 8=88$.

Answer:

88