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!
