Question

A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthor 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.

Answer 1

The proporion of wand prices lower then the blackthron wand is 0.1151

Explanation:

Normal Distribution

Also known as the Bell Curve by its characteristic shape where most values are concentrated in the center of the curve and they are rapidly spread out through both tails.

The parameters needed to compute probabilities with the normal distribution are: the mean
`\mu` and the standard deviation
`\sigma`. The curve is often called as N(
`\mu`,
`\sigma`).

The values of the probabilities are usually given in tables or computed by digital means like Excel or any online calculator. We'll use the Excel Normal Distribution formula

NORM.DIST(x,mean,standard_dev,cumulative)

This formula gives the left tail of the curve, i.e. P(x<X). The values provided in the problem are

`\mu = 50`

`\sigma=4`

`X=45.20`

The formula will be applied like this

NORM.DIST(45.20,50,4,TRUE)

It gives the value

P(x<45.20)=0.1151

The proporion of wand prices lower then the blackthron wand is 0.1151