Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 29.8 kilograms and standard deviation σ = 4.8 kilograms. Let x be the weight of a fawn in kilograms.

Convert the following x intervals to z intervals. (Round your answers to two decimal places.)

(a)    x < 30
z <

(b)    19 < x
< z

(c)    32 < x < 35
< z <

Convert the following z intervals to x intervals. (Round your answers to one decimal place.)

(d)    −2.17 < z
< x

(e)    z < 1.28
x <

(f)    −1.99 < z < 1.44
< x <

Answer 1

Question 1

Part a)

Standardizing the value
Z = ( X - µ ) / σ
Z = ( 30 - 29.8 ) / 4.8
Z = 0.0417

Z < 0.04

part b)

Standardizing the value
Z = ( X - µ ) / σ
Z = ( 19 - 29.8 ) / 4.8
Z = -2.25

-2..25 < Z

part c)

Standardizing the value
Z = ( X - µ ) / σ
Z = ( 32 - 29.8 ) / 4.8
Z = 0.4583

Z = ( 35 - 29.8 ) / 4.8
Z = 1.0833

0.46 < Z < 1.08

Part d)

X = µ + Zσ

X = 29.8 + ( - 2.17 ) * 4.8

X = 19.4

19.4 < X

Part e)

X = µ + Zσ

X = 29.8 + ( 1.28 ) * 4.8

X = 35.9

X < 35.9

Part f)

X1 = µ + Zσ = 29.8 + ( -1.99 ) * 4.8 = 20.2

X2 = µ + Zσ = 29.8 + ( 1.44 ) * 4.8 = 36.7

20.2 < X < 36.7