Question

x is a normally distributed random variable with mean 63 and standard deviation 7. what is the probability that x is between 56 and 70? use the 0.68-0.95-0.997 rule and write your answer as a decimal. round to the nearest thousandth if necessary.

Explanation:

Step1: Calculate z-scores for 56 and 70

For $x=56$: $z = \frac{56 - 63}{7} = -1$
For $x=70$: $z = \frac{70 - 63}{7} = 1$

Step2: Apply 0.68-0.95-0.997 rule

The rule states that 68% of data lies within $z=-1$ and $z=1$.

Answer:

0.680