type the correct answer in the box. use numerals instead of words. the mean of a normally distributed…
type the correct answer in the box. use numerals instead of words. the mean of a normally distributed dataset is 12, and the standard deviation is 2. % of the data points lie between 8 and 16.
Answer
Explanation:
Step1: Calculate the number of standard deviations from the mean
For (x = 8): (z=\frac{8 - 12}{2}=\frac{- 4}{2}=-2) For (x = 16): (z=\frac{16 - 12}{2}=\frac{4}{2}=2)
Step2: Use the empirical rule (68 - 95 - 99.7 rule)
The empirical 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