The vendor at Citi Field offers a health pack consisting ofapples and oranges. The weight, X, of an apple has a normaldistribution with a mean of 9 ounces and a standard deviation of0.6 ounces. Independent of this, the weight, Y, of an orange has anormal distribution with a mean of 7 ounces and a standarddeviation of 0.4 ounces. Suppose the health pack has a randomselection of 4 apples with weights
X1, X2, X3, X4
and 3 oranges with weights
Y1, Y2, Y3
. . Let Xsum be the sum of the apple weights in ounces and letYsum be the sum of the orange weights in ounces. W = Xsum + Ysum isthe random variable representing the total weight of the healthpack.
a) What is the probability that Xsum > 38?
b) What is the probability that Ysum > 22?
c) What is the expected value of Xsum?
d) What is the standard deviation of Xsum?
e) What is the variance of the random variable W?
f) What is the expected value of W?
g) What is the standard deviation of W?
h) What is the probability that W > 59 ounces?
i) i. If 100 health packs are sold what is the expected number soldwhich weigh more than 59 ounces?
