Question

Empirical Rule. It is known that the lengths of trout in a particular river are approximately mound-shaped with mean 14” and standard deviation 1”. About what proportion of the trout have lengths between 11' and 14' and 14” and 16”?

Answer 1

Answer)

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

Given mean = 14

S.d = 1

11 = 14 - (3*1)

17 = (14 + (3*1)

So, 99.7% lies in between 11 and 17

As normal distribution is symmetrical about mean

So, 99.7/2 = 49.85% lies in between 11 and 14

Between 14 and 16

16 = 14 + 2*1

So, 95/2 = 47.5% lies in between 14 and 16