Math 1431 – Spring 2003 – Test #1 – Practice
Question 8 Answer
  1. 74 inches = μ + 2σ. From the 68–95–99.7 rule we know that 95% of all observations fall between μ – 2σ and μ + 2σ (i.e., between 64 and 74). Thus, the area on both tails (i.e., below 64 and above 74) is the remaining 5%. Therefore, the area in each tail is 2.5%. So, only 2.5% of men are taller than 74 inches.
  2. From the 68–95–99.7 rule we know that 95% of all observations fall between μ – 2σ and μ + 2σ (i.e., between 64 and 74).
  3. 69.5 inches = μ – σ. From the 68–95–99.7 rule we know that 68% of all observations fall between μ – σ and μ + σ (i.e., between 66.5 and 71.5). Thus, the area on both tails (i.e., below 66.5 and above 71.5) is the remaining 32%. Therefore, the area in each tail is 16%. So, 16% of men are shorter than 66.5 inches.