Question

given: mean = 10, standard deviation = 2. what is the probability that the data will be between 4 and 16?

Explanation:

Step1: Calculate z - scores

For \(x = 4\), \(z_1=\frac{4 - 10}{2}=\frac{- 6}{2}=-3\). For \(x = 16\), \(z_2=\frac{16 - 10}{2}=\frac{6}{2}=3\).

Step2: Use the empirical rule

The empirical rule for a normal - distribution states that approximately 99.7% of the data lies within \(z=-3\) and \(z = 3\).

Answer:

1. 99.7%