7.82 Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm (“The Effects of Split Keyboard Geometry on Upper body Postures,” Ergonomics [2009]: 104–111).

a. What is the probability that a randomly selected typist’s speed is at most 60 wpm? less than 60 wpm?

b. What is the probability that a randomly selected typist’s speed is between 45 and 90 wpm?

c. Would you be surprised to find a typist in this population whose speed exceeded 105 wpm?

d. Suppose that two typists are independently selected.
What is the probability that both their typing speeds exceed 75 wpm?

e. Suppose that special training is to be made available to the slowest 20% of the typists. What typing speeds would qualify individuals for this training?