The grades on a math midterm at Springer are roughly symmetric with $\mu=72$ and $\sigma=4.5$.

Stephanie scored 86 on the exam.
Find the z-score for Stephanie's exam grade. Round to two decimal places.

Question

The grades on a math midterm at Springer are roughly symmetric with $\mu=72$ and $\sigma=4.5$.

Stephanie scored 86 on the exam.
Find the z-score for Stephanie's exam grade. Round to two decimal places.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the difference between Stephanie's score and the mean. ‖ ‖ $z = \frac{X - \mu}{\sigma}$ where $X = 86$, $\mu = 72$, and $\sigma = 4.5$. ‖ ‖ step 2 ⋮ Substitute the given values into the z-score formula. ‖ ‖ $z = \frac{86 - 72}{4.5}$ ‖ ‖ step 3 ⋮ Compute the numerator of the z-score formula. ‖ ‖ $86 - 72 = 14$ ‖ ‖ step 4 ⋮ Divide the difference by the standard deviation. ‖ ‖ $z = \frac{14}{4.5}$ ‖ ‖ step 5 ⋮ Calculate the z-score and round to two decimal places. ‖ ‖ $z = 3.111111111111111...$ ‖ ‖ $z \approx 3.11$ (rounded to two decimal places) ‖ ∻Answer∻ ⚹ $z = 3.11$ ⚹ ∻Key Concept∻ ⚹Z-score Calculation⚹ ∻Explanation∻ ⚹The z-score represents the number of standard deviations a data point is from the mean. It is calculated by subtracting the mean from the data point and then dividing by the standard deviation.⚹◊What is the formula to calculate the z-score for Stephanie's exam grade given $\mu=72$ and $\sigma=4.5$?⍭ Generate me a similar question◊

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