Question

During the summer of 2014, Coldstream Country Club in Cincinnati, Ohio collected data on 443 rounds of golf played from its white tees. The data for each golfer’s score on the twelfth hole are contained in the DATAfile Coldstream12. a. Construct an empirical discrete probability distribution for the player scores on the twelfth hole. b. A par is the score that a good golfer is expected to get for the hole. for hole number 12, par is four. What is the probability of a player scoring less than or equal to par on hole number 12? c. What is the expected score for hole number 12? d. What is the variance for hole number 12? e. What is the standard deviation for hole number 12?

here is each golfers score

Hole 12 Score
6
7
5
7
5
5
5
4
5
5
5
5
5
4
5
5
5
7
5
7
7
5
6
5
5
5
6
5
6
5
6
5
5
5
6
5
5
6
5
6
5
5
6
5
6
6
6
4
3
4
6
8
6
6
6
4
6
5
6
5
6
6
6
6
4
5
5
5
5
7
5
6
5
6
5
4
6
5
5
5
5
5
7
5
5
4
5
5
6
6
5
5
6
5
5
4
6
5
5
5
5
5
6
5
5
4
6
5
5
5
6
5
5
4
6
7
5
5
5
6
4
6
4
5
7
6
6
4
5
4
5
6
6
5
5
5
6
5
5
5
6
4
4
5
5
4
5
8
5
4
5
6
5
4
6
6
5
4
5
6
5
5
4
6
6
6
4
5
6
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6
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5
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6
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6
6
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6
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6
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6
6
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6
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6
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5
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6
5
4
8
6
5
5
5
5
6
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6
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6
6
4
5
6
4
5
5
7
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5
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6
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6
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4
6
5
5
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6
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5
7
6
5
6
5
5
8
5
3
6
6
6
6
5
3
6
7
5
5
4
6
5
6
5
5
4
5
5
7
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5
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5
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6
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5
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7
6
4
5
6
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5
5
4
4
6
4
5
5
7
5
5
6
4
5
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4
6
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6
5

Answer 1

Answer:

Step-by-step explanation:

Hello!

You have the data on 443 rounds of golf played on the 12th hole.

The variable of interest is:

X: score of one round of golf played on the 12th hole.

To construct the empirical distribution of the discrete variable you have to organize the data from least to highest and count how many times each score was recorded, establishing the absolute frequency for each value of the variable.

a. Check attachment.

fi= absolute frequency

Fi= accumulated absolute frequencies

hi= relative frequency

Hi= accumulated relative frequency

b.

P(X≤4)

This is the probability of the player scoring "4 or less", so it includes the probability of the player scoring 3 and the player scoring 4, symbolically:

P(X≤4)= P(X=3)+P(X=4)= H(4)= 0.136

c.

The expected score of a discrete variable is:

E(X)= [∑(Xi*fi)]/n= 2343/443= 5.29

d.

To calculate the variance of the variable you have to use the following formula:

V(X)= 1/(n-1)*[∑(Xi²*fi)-(∑(Xi*fi)²]/n)] = (1/442)*[12831-(2343²/443)]

V(X)= 0.993

e.

The standard deviation is the square root of the variance:

√V(X)=√0.993= 0.994

I hope it helps!

Answer 2

Answer:

Step-by-s

Step-by-step explanation: