A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is kno
wn 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.
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:
From the normal distribution table, the 9th percentile (0.09) corresponds to a z score of -1.34
The dye amount that represents the 9th percentile of the distribution is 4.464 ml