Chapter PIII, Problem 44RE

(a)

To determine

To Calculate: the scores of golf using the simulations on the basis of given data.

Answer to Problem 44RE

3

Explanation of Solution

There are advised that a golfer hitting a par-3 hole hopes to land on the green with a tee shot. The very first putt does not go in, but really the second putt should just go in. on the basis of the given assumptions, there is need to decide number of strokes it would really take:

-80 percent of the time, the tee shot lands on the green.

- 90% of the time, corresponding approaching shots land on the green.

At the moment, the first putt went at 20 percent, and successive puns go 90 percent of the time.

In order to estimate the golfer 's score, we must use a simulation. Based on the given probabilities, we can generate random numbers from 1 to 100 for each shot and compute the score. For instance, If the number is equal to or below 80, the tee shot will land on the green.

Random simulations are always the outcomes below:

Simulations	Number of Strokes
1	3
2	4
3	3
4	2
5	2
6	4
7	3
8	3
9	3
10	3

Now, by using the ten strokes and dividing it by the number of simulations, it could calculate the average of the strikes in the 10 simulations.

$\begin{array}{c}\text{Average}\text{=}\frac{\text{\#}\text{of}\text{Strokes}}{\#of\text{Simulations}}\end{array}$

  $\begin{array}{c}\text{=}\frac{3+4+3+2+2+4+3+3+3+3}{10}\end{array}$

  $\begin{array}{c}=3.0\end{array}$

Therefore, it would require 3.0 strokes to finish the hole on average.

(b)

To determine

To Calculate: the scores of golf using the simulations on the basis of given data.

Answer to Problem 44RE

5

Explanation of Solution

There are advised that a golfer hitting a par-5 hole tees off, hitting the ball throughout the fairway, hitting the green with an approach shot. So, the first putt would possibly not go in, so it should be the second putt. on the basis of given assumptions, there is require to decide number of strokes it really takes at night:

-70% of a time, the tee shot hits the fairway.

10 percent of the time, the second shot would strike the green and enter the fairway 60 percent of the time. The golfer should hit an action shot when it does not strike the green.

The 1st approach shot lands 80 percent of the time from of the fairway on the green. But otherwise, just 40 per cent of the time.

-Consequent target shots land 90 percent of the time on the green

The very first putt goes 20 percent of the time, and 90 percent of the time the following putts go.

To evaluate the scores of golfers, there is need to use a simulation. on the basis of given probabilities, it could randomly generate starting from 1 to 100 for every shot and compute the score. For instance, if the amount is equivalent or less than 70, the tee shot would reach the fairway.

Here are the outcomes of 10 arbitrary simulations:

Simulations	Number of Strokes
1	4
2	5
3	4
4	6
5	6
6	4
7	6
8	5
9	5
10	5

$\begin{array}{c}\text{Average}\text{=}\frac{\text{\#}\text{of}\text{Strokes}}{\#of\text{Simulations}}\end{array}$

  $\begin{array}{c}\text{=}\frac{4+5+4+6+6+4+6+5+5+5}{10}\end{array}$

  $\begin{array}{c}=5\end{array}$

Thus the, this would take 5.0 strikes to finish the holes on average.

(c)

To determine

To build: a set of assumptions that characterise the ability to play golf and then simulate the score on a few holes and clearly illustrate the simulation.

Answer to Problem 44RE

5.1

Explanation of Solution

On the basis the provided assumptions, there is need to decide number of strokes it would really take to accomplish a par-4 hole:

50% of the time, the tee shot strikes the fairway.

This first tee shot falls on the green 65 percent of the time from of the fairway, but otherwise only 30 percent of the time.

Corresponding chip shots land 80 percent of the time on the green.

The first putt takes place 10% of the time, and succeeding putts take place 75% of the time.

To calculate the golfer score, there is require to use a simulation. For every shot, it could arbitrarily select numbers from 1 to 100, on the basis of provided probability, and determine the score. For instance, if the number is equal or less than 50, the tee shot would reach the fairway.

Here are the outcomes of ten arbitrary simulations:

Simulations	Number of Strokes
1	6
2	5
3	4
4	5
5	6
6	5
7	4
8	4
9	6
10	6

$\begin{array}{c}\text{Average}\text{=}\frac{\text{\#}\text{of}\text{Strokes}}{\#of\text{Simulations}}\end{array}$

  $\begin{array}{c}\text{=}\frac{6+5+4+5+6+5+4+4+6+6}{10}\end{array}$

  $\begin{array}{c}=5.1\end{array}$

Therefore, this would require 5.1 strikes to finish the holes on average.