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3 years ago

5

It takes 10 hours to fill a pool with the inlet pipe. it can be emptied in 15 hours with the outlet pipe. if the pool is 2/3 ful

l to begin with, how long will it take to fill it from there if both pipes are open?

1 answer:

Ostrovityanka [42]3 years ago

4 0

Let t be the time the pipes are running. Then:
n/10-n/15=1/3
3n-2n=10
n=10
It will take 10 minutes to fill 1/3 of the pool
☺☺☺☺

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Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

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This means that when Z has a pvalue of 0.075, X = 8. So when $Z = -1.44, X = 8$ . So

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$8 - \mu = -1.44\sigma$

$\mu = 8 + 1.44\sigma$

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

$1.44 = \frac{14 - \mu}{\sigma}$

$14 - \mu = 1.44\sigma$

$1.44\sigma = 14 - \mu$

Replacing in the first equation

$\mu = 8 + 1.44\sigma$

$\mu = 8 + 14 - \mu$

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$\mu = \frac{22}{2}$

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Standard deviation:

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$1.44\sigma = 14 - 11$

$\sigma = \frac{3}{1.44}$

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