A fruit grower grows both red and green apples which have masses that are normally distributed. The

Question

A fruit grower grows both red and green apples which have masses that are normally distributed. The mass of a randomly chosen red apple has mean $75$g and standard deviation $12.5$g. The mass of a randomly chosen green apple has mean of $55$g and standard deviation $10.5$g. Find the probability that the total mass of $3$ randomly chosen green apples exceeds twice the mean mass of $3$ randomly chosen red apples.[3] A red apple is considered “underweight” if it weighs less than $70$g. Red apples are packed into bags of $10$ for transportation to a supermarket. A bag is considered to have passed the quality test if it contains less than $2$ “underweight” apples. Calculate the probability that in a randomly chosen batch of $20$ bags of red apples, all the bags fail the quality test. [4]

Accepted Answer

(i) $0.741$ (ii) $0.147$

Solving for Parameters, Comparisons, and Multi-Stage Distribution Models

Solving for Parameters, Comparisons, and Multi-Stage Distribution Models