Question

1. A company produces an 80-ounce bag of carrots and the weight of a bag of carrots is normally distributed with mean 80 ounces with standard deviation 4.5 ounces.

(a) What is the probability that a randomly selected bag of carrots will weigh less than 72 ounces?

(b) It turns out that their bags of carrots vary so much in weight and people complained. The company wants to reduce their standard deviation. What is the appropriate standard deviation if the company wants 99.6% of their bags weighing between 78 ounces and 82 ounces?

Answer 1

a) Let X= be a random variable representing the weight of a bag.

Then X is normally distributed with mean 80 and standard deviation 4.5

Then

where Z is a standard normal random variable.

b) Let standard deviation should be

We know p(Z<-2.878)=0.002 then