Chapter 6 Q20

An alert student has noticed a mistake in the textbook answers. Here I've worked through Q20 from Chapter 6.

a.       a. We want the area to the left of 50, because the question asks for fewer than 50 hours. Use =norm.dist(50,77,20,true) to get 0.089

b.      b. We want more than 100, the area to the right of 100. Excel adds up from the left, so we need to subtract from 1. Use =1-norm.dist(100,77,20,true) to get 0.125

c.       c. The question asks for the “upper 20%”. We are asked to find a random variable which corresponds to this area. In other words, what is the value of the random variable X which separates the top 20% from the bottom 80%. We can use =norm.inv for this, but we will need to write =norm.inv(0.8,77,20) to get 93.83. If we had written =norm.inv(0.2,77,20) then the result would the value of the random variable X that separates the bottom 20% from the top 80%. Draw a sketch and make sure you get this. This posting on our blog might help make this clearer.