Dr. XY thinks he can guess your sex by only knowing your height. His rule is sim

Question

Dr. XY thinks he can guess your sex by only knowing your height. His rule is simple: if your height is greater than 172 cm he predicts you are male. If your height is less than 172 he predicts you are female. You look up the statistics for male and female heights around the world for 20 year olds (we are going to assume that height doesn’t change much after this age) and find that about 75% of males are greater than 172 cm and 20% of females are greater than 172 cm. (The worldwide sex ratio of males to females is 101:100.) What is the probability that a randomly chosen individual who is over 172 cm is a male? What is the probability that an individual who is under 172 cm is a female?

Explanation / Answer

First arrange the probabilities in table:

           >172             <172

Male   0.75             0.25

Female 0.20           0.80

From the above table determine:

The probability that a randomly chosen individual who is over 172 cm is a male: 0.75

The probability that an individual who is under 172 cm is a female: 0.80

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