Three students take equivalent stress tests. Which is the highest relative score?

a. A score of 144 on a test with a mean of 128 and a standard deviation of 34.
b. A score of 90 on a test with a mean of 86 and a standard deviation of 18.
c. A score of 18 on a test with a mean of 15 and a standard deviation of 5.

34%

To determine which student has the highest relative score, we need to calculate the z-score for each student's score. The z-score indicates how many standard deviations a particular score is away from the mean.

The formula to calculate the z-score is:
z = (x - μ) / σ

Where:
z = z-score
x = student's score
μ = mean
σ = standard deviation

Let's calculate the z-scores for each student:

a. z = (144 - 128) / 34
a. z = 16 / 34
a. z ≈ 0.47

b. z = (90 - 86) / 18
b. z = 4 / 18
b. z ≈ 0.22

c. z = (18 - 15) / 5
c. z = 3 / 5
c. z = 0.6

Comparing the z-scores, we can see that the highest relative score is from student a, with a z-score of approximately 0.47.

To determine the highest relative score among the three students, we need to calculate the z-score for each score. The z-score measures how many standard deviations a particular score is away from the mean.

The formula to calculate the z-score is:
z = (x - μ) / σ

Where:
- x is the score
- μ is the mean
- σ is the standard deviation

Let's calculate the z-scores for each score:

1. For score a:
Mean (μ) = 128, Standard Deviation (σ) = 34, Score (x) = 144
Z-score (a) = (144 - 128) / 34 = 16 / 34 ≈ 0.471

2. For score b:
Mean (μ) = 86, Standard Deviation (σ) = 18, Score (x) = 90
Z-score (b) = (90 - 86) / 18 = 4 / 18 ≈ 0.222

3. For score c:
Mean (μ) = 15, Standard Deviation (σ) = 5, Score (x) = 18
Z-score (c) = (18 - 15) / 5 = 3 / 5 = 0.6

Now, we can compare the absolute values of the z-scores to determine which score has the highest relative score. The higher the absolute value of the z-score, the further away the score is from the mean.

Comparing the absolute values of the z-scores:
|Z-score (a)| ≈ 0.471
|Z-score (b)| ≈ 0.222
|Z-score (c)| = 0.6

The highest relative score is the one associated with the largest absolute value of the z-score, which in this case is the score from option c (Z-score ≈ 0.6). Therefore, the answer is option c - a score of 18 on a test with a mean of 15 and a standard deviation of 5.

According to a study by Stat & Associates PseudoScientific Consulting, the time interval between Atlantic hurricane of category 4 has a mean of 456 days and a standard deviation of 123 days. Suppose that you observe a sample of five (5) time intervals between successive category 4 hurricanes.

a. On average, what would you expect to be the mean of the five (5) time intervals?