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

Answer 1

Complete 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. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places

Answer:

0.1151

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = $45.20

μ is the population mean = $50

σ is the population standard deviation = $4

We are solving for x < 45.20

Hence:

z = 45.20 - 50/4

z = -1.2

Probability value from Z-Table:

P(x<45.20) = 0.11507

Approximately to 4 decimal places = 0.1151

Therefore, the proportion of wand prices that are lower than the price of the blackthorn wand is 0.1151