Question

question 7
the scores on an examination have a normal distribution. the mean of the scores is 50, and the standard deviation is 4. what is the best approximation of the percentage of students who can be expected to score between 46 and 54?
68%
95%
34%
50%

Explanation:

Step1: Calculate the number of standard deviations

The mean $\mu = 50$, standard deviation $\sigma=4$.
For $x = 46$, $z=\frac{46 - 50}{4}=\frac{- 4}{4}=-1$.
For $x = 54$, $z=\frac{54 - 50}{4}=\frac{4}{4}=1$.

Step2: Use the empirical rule

The empirical rule (68 - 95 - 99.7 rule) for a normal distribution states that approximately $68\%$ of the data lies within $z=-1$ and $z = 1$ (i.e., within $1$ standard deviation of the mean).

Answer:

68%