Question

2. I play golf. My score for one round is normally distributed with a mean of 72 with a standard deviation of 1.5. Tiger Woods plays golf. Tiger’s score for one round is normally distributed with a mean of 70.5 and a standard deviation of 1.
   1. If we play one round of golf against each other, what is the probability that I beat him? (4)

2. A typical golf tournament is 4 rounds of golf. If we play in a tournament against each other, what is the probability that I beat him? (4)

3. When the weather is bad it does two things to golf scores. First it adds two strokes to everyone’s scores for a round of golf. Second, it doubles everyone’s standard deviation. If I play against Tiger in a golf tournament, in bad weather, what is the probability that I beat him? (4)

Answer 1

Let X denote the my score and Y denote Tiger's score.

a)

Now,

Required probability =

b)

Now,

Required probability =

c)

Now,

So,

Required probability =