Question

2. At a zoo, Biteyfloofers have a mean length of 11” and standard devation 2.5”, while Fluffersnappers have a mean length of 10” and standard deviation 2”. Both follow an approx. normal distribution. (a) Which is more unusual, a Fluffersnapper that is 12” long or a Biteyfloofer that is 12”? (b) Which would seem longer relative to their populations, a 9” Fluffersnapper or a 9.5” Biteyfloofer? (c) Use the empirical rule to compare the middle 95% of heights for each creature.

Answer 1

This is a normal distribution question with

Biteyfloofers

]a) x = 12

P(x > 12.0)=?

The z-score at x = 12.0 is,

z = 0.4

This implies that

P(x > 12.0) = P(z > 0.4) = 1 - 0.6554217416103242

P(x > 12.0) = {0.3446}

Biteyfloofer

P(x > 12.0)=?

The z-score at x = 12.0 is,

z = 1.0

This implies that

P(x > 12.0) = P(z > 1.0) = 1 - 0.8413447460685429

P(x > 12.0) = {0.1587}

b)

x = 9.5

P(x < 9.5)=?

The z-score at x = 9.5 is,

z = {9.5-11.0}/{2.5}

z = -0.6

Fluffersnapper

1P(x < 9.0)=?

The z-score at x = 9.0 is,

z = {9.0-10.0}/{2.0}

z = -0.5

Relatively Fluffersnapper is larger

c)

P(x<X < x) = 0.95

This implies that

by emperical rule

Biteyfloofers

Fluffersnapper