Question

x is a normally distributed random variable with mean 28 and standard deviation 20. what is the probability that x is between 16 and 49? write your answer as a decimal rounded to the nearest thousandth.

Explanation:

Step1: Calculate z-score for 16

The formula for z-score is $z = \frac{x - \mu}{\sigma}$, where $\mu$ is the mean and $\sigma$ is the standard deviation. For $x = 16$, $\mu = 28$, $\sigma = 20$.
$z_1=\frac{16 - 28}{20}=\frac{- 12}{20}=- 0.6$

Step2: Calculate z-score for 49

For $x = 49$, using the same formula:
$z_2=\frac{49 - 28}{20}=\frac{21}{20} = 1.05$

Step3: Find probabilities from z-table

We need to find $P(-0.6

Step4: Calculate the difference

$P(-0.6

Answer:

0.579