A fresh produce distributor has received complaints that his
bananas have been arriving at the
retail sale store. He is suspicious of the complaint, since
his average delivery time is only 4 days
(96 hours), and the bananas are fresh at the time of shipment.
He decides to simulate the
appropriate conditions and make a test to see how long it
takes before the bananas become
spoiled. He selects at random a sample of four crates of
bananas and measures the number of
hours before spoilage occurs. The results for number of hours,
x, are given as 106.102. 104, and
108.
a) Find the mean hours before spoilage.
b) Find the standard deviation for x.
c) On the basis of these measures, do you think that many of
the bananas may indeed be
arriving spoiled, or are you also suspicious of the
complaints? Explain.
d) Find the range of the sample of x values.
e) Why is the answer to part b is better than the answer to
part d as an estimate of the
dispersion for the entire population of bananas from which the
sample was taken?