Answer to Question #294413 in Statistics and Probability for Gio

Question

Five hundred children participated in a field demonstration. Their heights averaged 110 cm

with a standard deviation of 6 cm,

a. What is the probability that a child, picked at random, has a height greater than 116 cm?

b. What is the probability that the height of a child, picked at random, is less that 104 cm?

c. How many children belong to the upper 15% of the group?

Answer 1

a. $P(X>116)=P(Z>\frac{116-110}{6})=P(Z>1)=1-P(Z<1)=0.1587.$

b. $P(X<104)=P(Z<\frac{104-110}{6})=P(Z<-1)=0.1587.$

c. $N=600*0.15=75.$