Question

Provided are the SAT mathematics scores of a random sample of seven students selected from the freshman class at Georgia Southern University. 470 690 540 570 470 680 710

Compute the mean from the first bootstrap samples. Give your answer to one decimal place.

Answer 1

The z-score for an SAT score of 720 is 1.7391, which means it is higher than about 96.55% of the scores. A math SAT score of 692.5 is 1.5 standard deviations above the mean, indicating a relatively high performance.

Step-by-step explanation:

The z-score for an SAT score of 720 can be calculated as:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

Using the given values of μ = 520 and σ = 115, the z-score for a score of 720 is:

z = (720 - 520) / 115 = 1.7391

This means that a score of 720 is 1.7391 standard deviations above the mean. In other words, it is higher than about 96.55% of the scores.

The math SAT score that is 1.5 standard deviations above the mean can be calculated as:

x = μ + (z * σ)

Using the given values of μ = 520, σ = 115, and z = 1.5, the math SAT score is approximately 692.5.

This score is 1.5 standard deviations above the mean and indicates a relatively high performance.