Question

x is a normally distributed random variable with mean 28 and standard deviation 8. what is the probability that x is between 12 and 52? 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-score for 12

$z_1 = \frac{12 - 28}{8} = -2$

Step2: Calculate z-score for 52

$z_2 = \frac{52 - 28}{8} = 3$

Step3: Apply 0.68-0.95-0.997 rule

For $z=-2$ to $z=2$: probability = 0.95; For $z=2$ to $z=3$: $\frac{0.997 - 0.95}{2} = 0.0235$
Total probability = $0.95 + 0.0235 = 0.9735$

Answer:

0.974