Exercise 1. A botanical study divides a forested region into 446 microenvi- ronm
ID: 3044163 • Letter: E
Question
Exercise 1. A botanical study divides a forested region into 446 microenvi- ronments. Two qualities are determined for each microenvironments. The first, abbreviated A, is that a certain plant is plentiful in that area. The second B is that a certain lizard is active (reflected in the scat traces) in the area. Suppose . 191 microenvironments are of type A, . 285 microenvironments are of type B, and . 128 microenvironments are of type A and B. (A) Briefly describe the sample set. (B) How many type A microenvironments were not of type B? (C) How many type B microenvironments were not of type A? (D) How many microenvironments were either of type A, or of type B (or of both types)? (E) What, to the nearest percent, is the relative frequency of type B mi- croenvironments? (F) What, to the nearest percent, is the relative frequency of microenvi- ronments which are neither type A nor type B?Explanation / Answer
a) A = 191, B = 285
A B = 128
A B = A + B - (A B)
= 191+285-128 = 348
neither A nor B = 446-348 = 98
b) A but not B => A - (A B) = 191-128 = 63
c) B but not A => B - (A B) = 285-128 = 157
d)either A or B = A B = 3488
e) percent relative frequency of B = (Count B / total) *100
= (285/446) * 100 = 63.90%
Rounding off to 64%
f)
percent relative frequency of neither A nor B = (Count neither A nor B / total) *100
= (98/446) * 100 = 21.97%
Rounding off to 22%
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