For Exercises 4.14 and 4.15, see pages 180–181; for 4.16 to 4.20, see pages 183–184; for 4.21 to 4.23, see pages 185–186; for 4.24, see page 187; for 4.25 and 4.26, see page 189; and for 4.27 to 4.29, see page 190.

Question 4.21

4.21 Household space heating.

Draw a U.S. household at random, and record the primary source of energy to generate heat for warmth of the household using space-heating equipment. “At random” means that we give every household the same chance to be chosen. That is, we choose an SRS of size 1. Here is the distribution of primary sources for U.S. households:5

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Primary source Probability
Natural gas 0.50
Electricity 0.35
Distillate fuel oil 0.06
Liquefied petroleum gases 0.05
Wood 0.02
Other 0.02
  1. Show that this is a legitimate probability model.
  2. What is the probability that a randomly chosen U.S. household uses natural gas or electricity as its primary source of energy for space heating?

4.21

(a) (b) 0.85.