Question

a set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. a blackthorn wand has a price of 45.20 dollars. what proportion of wand prices are lower than the price of the blackthorn wand? you may round your answer to four decimal places.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 50$, $\sigma=4$, and $x = 45.20$.
$z=\frac{45.20 - 50}{4}=\frac{- 4.8}{4}=-1.2$

Step2: Find the proportion from the z - table

We look up the z - score of $-1.2$ in the standard normal distribution table. The value corresponding to $z=-1.2$ in the standard normal table gives the proportion of values less than $x = 45.20$. From the standard normal table, the value for $z=-1.2$ is $0.1151$.

Answer:

$0.1151$