Question

The weight of a species of cat follows the normal distribution with the mean of 32kg and the standard deviation of 5kg. 

 

a) One cat of that species is encountered, find the probability that the cat i) weights more than 37kg.                                                    ii) weights between 30kg and 35kg.

Answer 1

$Given \; that, μ=32, σ=5, then,\\ i) P(x>37) = P( Z >\frac{37-32}{5})\\ =P(Z>1)\\=0.5- P(0<Z<1)=0.5-0.3413=0.1587\\ ii) P(30<x<35) = P(\frac{30-32}{5}< Z >\frac{35-32}{5})\\ =P(-0.4<Z<0.6)\\= P(0<Z<0.4)+P(0<Z<0.6)\\ =0.1554+0.2257=0.3811\\$