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julia-pushkina [17]
3 years ago
15

HELP PLEASE....... FYI: 33 points

Mathematics
1 answer:
makvit [3.9K]3 years ago
3 0
The first question is square or rectangle
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A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is kno
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Answer:

The 90th percentile of the distribution is 6.512 ml.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 6 milliliters (ml) and a standard deviation of 0.4 ml.

This means that \mu = 6, \sigma = 0.4

Find the dye amount that represents the 90th percentile (i.e. 90%) of the distribution.

This is X when Z has a p-value of 0.9, so X when Z = 1.28. Then

Z = \frac{X - \mu}{\sigma}

1.28 = \frac{X - 6}{0.4}

X - 6 = 1.28*0.4

X = 6.512

The 90th percentile of the distribution is 6.512 ml.

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