Question

Weights of students are normally distributed with a mean of 55 kg and a variance of 9 kg.
a. Find the probability that the weight of one randomly selected student is less than 48 kg.
b. Find the probability that the mean weight of 16 randomly selected students is more than 57 kg.
c. Find the median of the weight of students

Answer 1

a. $P(X<48)=P(Z<\frac{48-55}{9})=P(Z<-0.78)=0.2177.$

b. $P(\bar X>57)=P(Z>\frac{57-55}{\frac{9}{\sqrt{16}}})=P(Z>0.89)=0.1867.$

c. $P(Z<z)=0.5\to z=0\to \frac{x-55}{9}=0\to x=55.$

Median weight is 55 kg.