Question

assume a normal distribution of scores has a mean of 52 and a standard deviation of 4. what is the range of the middle 95% of the distribution?
o 48 - 56
o 44 - 60
o 40 - 64
o 48 - 60

Explanation:

Step1: Recall the property of normal distribution

For a normal distribution, the middle 95% of the data lies within 2 standard - deviations of the mean.

Step2: Calculate the lower bound

The lower bound is $\mu - 2\sigma$, where $\mu = 52$ and $\sigma = 4$. So, $52-2\times4=52 - 8 = 44$.

Step3: Calculate the upper bound

The upper bound is $\mu + 2\sigma$, where $\mu = 52$ and $\sigma = 4$. So, $52 + 2\times4=52+8 = 60$.

Answer:

44 - 60