Question

μ=220 grams σ=25 grams

If a mango is selected at random, what is the probability that its weight lies between 180 and 250 grams?

Answer 1

We have a normal distribution, $\mu=220, \sigma=25.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}.$

$z_1=\cfrac{180-220}{25}=-1.60;\\ z_2=\cfrac{250-220}{25}=1.20;\\ P(180<X<250)=\\ =P(-1.60<Z<1.20)=\\ =P(Z<1.20)-P(Z<-1.60)=\\ =0.8849-0.0548=0.8301\\ \text{ (from z-table)}.$