Question

The customer account at a certain department store has an average balance of 480 kwacha and the standard deviation of 160 kwacha. Assuming normal distribution, What proportion of the account is between 240 and 360.

Answer 1

$P(240<X<360)=P(\frac{240-480}{160}<Z<\frac{360-480}{160})=P(-1.5<Z<-0.75)=$

$=P(Z<-0.75)-P(Z<-1.5)=P(Z<1.5)-P(Z<0.75)=$

$=0.9332-0.7734=0.1598.$