Find three mixed numbers so that the sum is 18 and the difference between the greatest number and least number is 5 1/5

1 answer:

7 0

Suppose y=0. That means
x+z = 18 
x-z = 26/5 

x = 58/5 
z = 32/5 

So, the largest x can be is 58/5 
Now, suppose we toss in y. If we subtract y/2 from both x and z, then the difference between x and z is still 26/5, and the sum is 

(x-y/2) + y + (z-y/2) = x+z = 18 

For example, if y = 4, 

x = 48/5 
y = 20/5 
z = 22/5 

x-z is still 26/5, and the sum is still 18.

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The mean is 9.65 ohms and the standard deviation is 0.2742 ohms.

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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 X = 10.634, Z has a pvalue of 1-0.1 = 0.9. So when X = 10.634, Z = 1.28.

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$1.28 = \frac{10.634 - \mu}{\sigma}$