It was rumored that Britain’s domestic intelligence service MI5 has an upper limit on the height of its spies, on the assumption that tall people stand out (although MI5 denies it). The rumor said that, to apply to be a spy, you can be no taller than 5 feet 11 inches (180.3 cm) if you are a man, and no taller than 5 feet 8 inches (172.7 cm) if you are a woman (supposedly to allow the spies to blend in with a crowd).

a. If the mean height of British men is 177.0 cm, with standard deviation 7.1 cm, what proportion of British men would be precluded from being spies by this hypothetical height restriction? Assume that height follows a normal distribution.

b. The mean height of women in Britain is 163.3 cm, with standard deviation 6.4 cm. Assuming a normal distribution of female height, what fraction of women meet the height standard for application to MI5?

c. Sean Connery, the original James Bond in the movies, is about 183.4 cm tall. By how many standard deviations does he exceed the height limit for spies?