Question

the weight of a dart to be used in a tournament is normally distributed with a mean of 17gms and a standard deviation of 0.3gms. find the probability that a dart choose at random has it weight between 16.55gms and 17.45gms 

Answer 1

$z=\frac{x-\mu}{\sigma}$

$z_1=\frac{16.55-17}{0.3}=-1.5$

$z_2=\frac{17.45-17}{0.3}=1.5$

$P(16.55<x<17.45)=P(z_1<z<z_2)=P(z<1.5)-P(z<-1.5)=$

$=0.9332-0.0668=0.8664$