Question

x is a normally distributed random variable with mean 25 and standard deviation 22. what is the probability that x is between 6 and 44? write your answer as a decimal rounded to the nearest thousandth.

Explanation:

Step1: Recall the Z - score formula

The Z - score formula is $Z=\frac{X - \mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $X$ is the value from the original distribution.
For $X = 6$, $\mu=25$, $\sigma = 22$:
$Z_1=\frac{6 - 25}{22}=\frac{- 19}{22}\approx - 0.86$
For $X = 44$, $\mu = 25$, $\sigma=22$:
$Z_2=\frac{44 - 25}{22}=\frac{19}{22}\approx0.86$

Step2: Find the probabilities for the Z - scores

We need to find $P(-0.86Using the standard normal distribution table (or a calculator with normal distribution functions):
$P(Z < 0.86)\approx0.8051$
$P(Z < - 0.86)\approx0.1949$

Step3: Calculate the probability

$P(-0.86

Answer:

0.610