Write the answer and then explain it.

Question 1

A mango fruit processing factory that uses robots to sort fruit based on fruit weight. Based on previous information, mango fruit weight (X) has a normal distribution with an average value of = 300 grams and a standard deviation of = 100 grams. The robot is programmed to be able to separate the weight of mangoes with the following criteria:

Fruit quality A, if X < -

Fruit quality B, if - < X < +0,5 Fruit quality C, if X > + 0.5

a. What percent of mangoes weigh more than 450 grams? b. If the 10 percent of the lightest fruit will be made into juice products, what is the weight limit for mangoes that will be made into juice? c. If at any time there are 1000 mangoes available, how many of each quality A, B and C are available?