Given the following information about a sample, calculate a z score for a test grade of 91.

= 87, s = 4.01

I assume the median is 87

z-score = (91-87)/4.01
= ....

Why did the test grade go to the circus? Because it wanted to join the z-scored circus!

But in all seriousness, let's calculate the z-score. The z-score formula is:

z = (x - μ) / σ

Where:
- x is the value you want to standardize (in this case, the test grade of 91)
- μ is the mean (average) of the sample (in this case, 87)
- σ is the standard deviation of the sample (in this case, 4.01)

Plugging in the values:

z = (91 - 87) / 4.01

Calculating:

z = 4 / 4.01

z ≈ 0.998 (rounded to three decimal places)

So the z-score for a test grade of 91 is approximately 0.998.

To calculate the z-score, we'll use the formula:

z = (x - μ) / σ

Where:
x = the value we want to calculate the z-score for (test grade of 91)
μ = the mean of the sample (given as 87)
σ = the standard deviation of the sample (given as 4.01)

Plugging in these values into the formula, we get:

z = (91 - 87) / 4.01

Simplifying this expression, we have:

z = 4 / 4.01

Calculating this further, we get:

z ≈ 0.99750623

Therefore, the z-score for a test grade of 91, given the sample mean of 87 and standard deviation of 4.01, is approximately 0.9975.

To calculate the z-score for a test grade of 91, you will need the mean (µ) and the standard deviation (σ) of the sample.

In this case, you are given the mean (µ) = 87 and the standard deviation (σ) = 4.01.

The formula to calculate the z-score is:

z = (X - µ) / σ

where X is the given value, µ is the mean, and σ is the standard deviation.

Now, let's substitute the values into the formula:

z = (91 - 87) / 4.01

z = 4 / 4.01

z ≈ 0.997

Therefore, the z-score for a test grade of 91, given a mean of 87 and a standard deviation of 4.01, is approximately 0.997.