{"id":74,"date":"2018-10-18T14:11:58","date_gmt":"2018-10-18T14:11:58","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=74"},"modified":"2018-10-18T14:11:58","modified_gmt":"2018-10-18T14:11:58","slug":"how-tall-is-a","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2018\/10\/18\/how-tall-is-a\/","title":{"rendered":"How tall is A?"},"content":{"rendered":"

Here are a series of problems I posed in my Bayesian statistics class:<\/p>\n

1) Suppose you meet an adult resident of the U.S. who is 170 cm tall. What is the probability that they are male?<\/p>\n

2) Suppose I choose two U.S. residents at random and A is taller than B.\u00a0 How tall is A?<\/p>\n

3)\u00a0In a room of 10 randomly chosen U.S. residents, A is the second tallest.\u00a0 How tall is A?\u00a0 And what is the probability that A is male?<\/p>\n

As background: For adult male residents of the US, the mean and standard deviation of height are 178 cm and 7.7 cm. For adult female residents the corresponding stats are 163 cm and 7.3 cm.\u00a0 And 51% of the adult population is female.<\/p>\n

If you solve the problems in order, you can reuse code from the first two to solve the third.<\/p>\n

Here’s my solution, using a grid algorithm and the libraries from Think Bayes<\/em>:<\/p>\n