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ratelena [41]
3 years ago
12

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.
Mathematics
1 answer:
Anton [14]3 years ago
5 0

Answer:

4.464 ml

Step-by-step 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=\frac{x-\mu}{\sigma}

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

z=\frac{x-\mu}{\sigma}\\\\-1.34=\frac{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

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