Assume that the U.S. Open Golf Tournament was played at Congressional Country Club, with prizes ranging from $465,000 for first place to $5,000. Par for the course is 70. The tournament consists of four rounds played on different days. Suppose the scores for each round of the 32 players who placed in the money (more than $17,000) were given on a website.

The scores for the first round were as follows:
74, 65, 67, 73, 74, 73, 71, 71, 74, 73, 67, 68, 75, 71, 72, 71, 65, 70, 71, 71, 74, 73, 66, 75, 70, 65, 71, 72, 72, 73, 71, 67.

The scores for the fourth round for these players were as follows:
75, 69, 74, 74, 72, 72, 70, 71, 71, 70, 73, 75, 73, 72, 71, 71, 72, 70, 70, 71, 72, 72, 74, 72, 72, 68, 69, 70, 69, 71, 73, 74.

1) Compare the two distributions and choose the right answer below:
A. Scores are equal for both the rounds.
B. Scores are lower in the fourth round.
C. Scores are lower in the first round.

In order to compare the two distributions, we need to look at the averages (or means) of the scores for each round. We can calculate these by summing up all the scores and dividing by the number of scores.

For the first round:

Sum of scores = 74 + 65 + 67 + ... + 71 + 67 = 2262
Number of scores = 32
Average score = 2262 / 32 ≈ 70.6875

For the fourth round:

Sum of scores = 75 + 69 + 74 + ... + 69 + 71 + 73 + 74 = 2351
Number of scores = 32
Average score = 2351 / 32 ≈ 73.4688

Therefore, the scores are higher in the fourth round.

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