How do I find the proportion

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Lengths of fish caught by a commercial fishing boat have a bell-shaped distribution with mean 23 inches and standard deviation 1.5 inches.

1. About what proportion of all fish caught are between 20 inches and 26 inches long?
2. About what proportion of all fish caught are between 20 inches and 23 inches long?
3. About how long is the longest fish caught (only a small fraction of a percent are longer)?
Oct 3rd, 2015

1.  Z(20 inches:) = (20-23)/1.5 = -3/1.5 = -2   which is 2 standard deviations to the left of the mean

Z(26 inches) = (26-23)/1.5 = 3/1.5 = 2   which 2 standard deviations to the right of the mean

In between those two measurements are 2 - (-2) = 4 standard deviations

According to the Normal Curve this represents a proportion of 95.4%

2.  Between 20 and 23 inches is exactly one half of the proportion between 20 and 26 inches

So the proportion is 47.7%

3.  The longest fish would be 3 standard deviations to the right of the mean:

Which would be a length of 23 + 3(1.5) = 23 + 4.5 = 27.5 inches

Sep 16th, 2015

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Oct 3rd, 2015
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Oct 3rd, 2015
Nov 23rd, 2017
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