Question

The Yankee Stadium food menu includes dirty fries and loaded fries. Let D be the weight, in ounces, of a randomly selected order of dirty fries. Let L be the weight, in ounces, of a randomly selected order of loaded fries. Suppose D is normally distributed with a mean weight of 5.2 ounces and a standard deviation of 0.4 ounces. Suppose L is normally distributed with a mean weight of 5.4 ounces and a standard deviation of 0.5 ounces. L and D are independent.

a) Calculate the expected value of L + D. (in ounces)  

b) Calculate the standard deviation of L + D. (in ounces)  

c) What is the probability that an order of loaded fries weighs less than 5 ounces?  

d) What is the probability that an order of loaded fries weighs between 5 and 6 ounces?  

e) What is the 95th percentile of D?  

f) What is the probability that L + D is greater than 11 ounces?  

g) Suppose we purchase an order of loaded fries and an order of dirty fries. What is the probability that each of the orders weighs more than 5 ounces? (L>5 and D>5)  

h) What is the probability that D is greater than L?  

Answer 1

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