Question

the scores on a test are normally distributed with a mean of 70 and a standard deviation of 14. 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 the mean and standard - deviation values

Mean $\mu = 70$, standard deviation $\sigma=14$.

Step2: Calculate the score above the mean

The score that is $\frac{1}{2}$ standard deviation above the mean is $x=\mu+\frac{1}{2}\sigma$. Substitute $\mu = 70$ and $\sigma = 14$ into the formula: $x=70+\frac{1}{2}\times14$.

Step3: Simplify the expression

First, calculate $\frac{1}{2}\times14 = 7$. Then, $70 + 7=77$.

Answer:

77