A Marketer of Holiday Fruit Boxes Has a New Order $= 2.54 \mathrm {~cm}$

Essay

A marketer of holiday fruit boxes has a new order for boxes that will hold 12 pieces of
fruit. The box is to hold 4 rows of fruit, each row consisting of an orange and two
apples. In addition to the fruit there will need to be protective packing lining the
box. The mean diameter of oranges is 3.0 inches and the standard deviation is 0.25
inches. The mean diameter of apples is 4.0 inches and the standard deviation is 0.2
inches. a) If the orange diameter information had been given in centimeters rather than inches, what would be the mean and standard deviation of the orange diameter? (Note: 1 inch $= 2.54 \mathrm {~cm}$ .)
b) Suppose apples are randomly chosen for a particular row of fruit. Define random variable $b = a _ { 1 } + a _ { 2 }$ to be the space needed -- in inches -- by two randomly selected apples. What are the mean and standard deviation of $b$ ? c) Suppose that an additional 4 inches of box width is specified for the orange and the protective packing. Let the random variable "box width" be defined as: $c = 4 + a _ { 1 } + a _ { 2 }$ . How do the mean and standard deviation of $b$ in part (b) differ from the mean and standard deviation of the random variable, c, defined here in part (c)? Do not recalculate the mean and standard deviation.