Question

A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. Find the dye amount that represents the 9th percentile of the distribution.

Answer 1

4.464 ml

Explanation:

Given that:

mean (μ) = 5 mm, standard deviation (σ) = 0.4 ml

The z score is a score in statistics used to determine by how many standard deviation the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if the z score is negative then the raw score is below the mean It is given by:

`z=(x-\mu)/(\sigma)`

From the normal distribution table, the 9th percentile (0.09) corresponds to a z score of -1.34

`z=(x-\mu)/(\sigma)\\\\-1.34=(x-5)/(0.4)\\\\x-5=-0.536\\\\x=5-0.536\\\\x=4.464`

The dye amount that represents the 9th percentile of the distribution is 4.464 ml