Question

The weights of a women population are normally distributed with mean 60kg and standard deviation 5kg. Find the probability that the weight of a woman chosen at random is between 61 and 65kg.

Answer 1

$\mu = 60$

$\sigma = 5$

$P(61<X<65)=P( \frac{61-\mu}{\sigma}<Z<\frac{65-\mu}{\sigma})=P( \frac{61-60}{5}<Z<\frac{65-60}{5})=P(0.2<Z<1) = P(Z<1) -P(Z<0.2)=0.8413-0.5793=0.262$

Answer: the probability that the weight of a woman chosen at random is between 61 and 65kg is 26.2%