Question

x is a normally distributed random variable with mean 49 and standard deviation 21. what is the probability that x is between 28 and 91? 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 28

$z_1 = \frac{28 - 49}{21} = -1$

Step2: Calculate z-score for 91

$z_2 = \frac{91 - 49}{21} = 2$

Step3: Apply empirical rule

The area for $z=-1$ to $z=0$ is $\frac{0.68}{2}=0.34$, and the area for $z=0$ to $z=2$ is $\frac{0.95}{2}=0.475$. Sum these areas.
$0.34 + 0.475 = 0.815$

Answer:

0.815