Question

question 6
on a standardized test, the mean is 48 and the standard deviation is 4. approximately what percent of the scores will fall in the range from 36 to 60?
68%
95%
99%
34%

Explanation:

Step1: Calculate the number of standard deviations from the mean

The formula for the number of standard deviations \(z=\frac{x - \mu}{\sigma}\), where \(\mu = 48\) (mean) and \(\sigma=4\) (standard deviation).
For \(x = 36\): \(z_1=\frac{36 - 48}{4}=\frac{- 12}{4}=-3\)
For \(x = 60\): \(z_2=\frac{60 - 48}{4}=\frac{12}{4}=3\)

Step2: Apply the empirical rule

The empirical rule (68 - 95 - 99.7 rule) for a normal distribution states that approximately \(P(\mu - 3\sigma<X<\mu + 3\sigma)\) covers about \(99.7\%\approx99\%\) of the data.

Answer:

99%