all of question 1

Exercise 1 Suppose that at Curtis Orchard: . All apple weights are independent, and apple weights of the same type are i. i.d. . The weight of Fuji apples is normally distributed with a mean of 150 grams and a standard deviation of 5 grams. Let F be the weight of a randomly selected Fuji apple. . The weight of Honeycrisp apples is normally distributed with a mean of 140 grams and a standard deviation of 6 grams. Let H be the weight of a randomly selected Honeycrisp apple. Show all your work and explicitly state the distributions used. a) (0.5 pt) Suppose you pick 5 Honeycrisp apples at random. Assuming independence, what is the probability that that the average weight of the 5 apples is less than 137 grams? b) (0.5 pt) Suppose you pick 10 Fuji apples at random. Assuming independence, what is the probability that that the total weight of the 10 apples is more than 1570 grams? c) (1 pt) Suppose you pick one Fuji and One Honeycrisp apple at random. What is the probability that the Fuji apple weighs less than the Honeycrisp apple? d) (1 pt) Suppose you pick 5 Honeycrisp apples and 5 Fuji apples. What is the probability that their total weight is less than 1500g