Aresearcher is interested in the lengths of salvelinus fontinalis (brook trout), which are known to be approximately normally distributed with mean 80 centimeters and standard deviation 5 centimeters. to preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught.
what proportion of fish are larger than 86 centimeters in length

a. 0.0228
b. 0.0548
c. 0.1151
d. 0.8849

c. 0.1151

Step-by-step explanation:

d) the probability that, on average, fish are larger than 86 centimeters in length.The area under part of a normal probability curve is  directly proportional to probability and the value is calculated as

z = (x₁−x) /σ

where z = propability of normal curve

x₁ = variate mean = 86cm

x = mean of 80cm

σ = standard deviation = 5cm

applying the formula,

z= (86-80)/5

z = 6/5 =1.2

Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 1.2 corresponds to an area of 0.3849 between the mean value. but, because the standard curve has 0.5, then will minus 0.3849 from 0.5= 0.5 - 0.3849 = 0.1151

Thus the probability of a fish are larger than 86 centimeters in length is 0.1151

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