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:

3. 99.7%