Question

question 8
on a standardized test, the mean is 68 and the standard deviation is 4.5. what is the best approximation of the percentage of scores that will fall in the range 59 - 77?
95%
68%
99%
34%

Explanation:

Step1: Calculate the number of standard deviations from the mean

For the lower bound \(59\):

$$z_1=\frac{59 - 68}{4.5}=\frac{-9}{4.5}=- 2$$

For the upper bound \(77\):

$$z_2=\frac{77 - 68}{4.5}=\frac{9}{4.5}=2$$

Step2: Use the empirical rule

The empirical rule (68 - 95 - 99.7 rule) for a normal distribution states that approximately \(95\%\) of the data lies within \(z=-2\) and \(z = 2\) (i.e., within \(2\) standard deviations of the mean).

Answer:

\(95\%\)