In poorer countries, growth of children can be an important indicator of general
ID: 3354362 • Letter: I
Question
In poorer countries, growth of children can be an important indicator of general levels of health and nutrition. In an article from an anthropological journal, it was suggested that the population of 5 year olds have heights approximately normally distributed with mean = 100 cm and SD = 6 cm. Answer the following using the normal curve approximation.
(A) What percent of the population of 5 year olds should have a height less than 96 cm?
- What is the z-score(s) you calculated?
- Would you be shading above, below, or between on the normal curve?
- What is the probability?
(B) What height is the 70th percentile in this population?
- What percentile is the unknown value in?
- What is the z-score for this percentile?
- What is the value?
(C) If a child were picked at random from this population, what is the % chance that the child’s height would be between 100 cm and 102 cm ?
- What is the z-score(s) you calculated?
- Would you be shading above, below, or between on the normal curve?
- What is the probability?
Explanation / Answer
=100
=6
a)
x=96
z=(x-)/
=(96-100)/6
=-4/6
=-0.67
We shade below
P(x<96 )=P(z<-0.67) =0.2514
b)
we have to find 70th percentile
z score for P=70% =0.7 is 0.5244
so x=z* +
x=0.5244*6 +100
=3.1464 +100
=103.1464
C)
for x=100
z=(x-)/
=(100-100)/6
=0/6
=0
for x=102
z=(x-)/
=(102-100)/6
=2/6
=0.33
We shade between on the normal curve
P(100<x<102) =P(0<z<0.33)
=P(z<0.33) -P(z<0)
=0.6293-0.5
=0.1293