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

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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

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