Z-Score Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
On Test A, Maria scored 7878 (ΞΌ=70\mu = 70, Οƒ=5\sigma = 5). On Test B, she scored 8585 (ΞΌ=80\mu = 80, Οƒ=10\sigma = 10). On which test did she perform relatively better?

Solution

  1. 1
    Test A z-score: zA=78βˆ’705=1.6z_A = \frac{78 - 70}{5} = 1.6.
  2. 2
    Test B z-score: zB=85βˆ’8010=0.5z_B = \frac{85 - 80}{10} = 0.5.
  3. 3
    Since zA>zBz_A > z_B, Maria performed relatively better on Test A.

Answer

TestΒ Aβ€…β€Š(z=1.6>0.5)\text{Test A} \; (z = 1.6 > 0.5)
Z-scores standardize values from different distributions, making them directly comparable. A higher z-score indicates a relatively stronger performance.

About Z-Score

A z-score measures how many standard deviations a data value is above or below the mean: z=(xβˆ’ΞΌ)/Οƒz = (x - \mu)/\sigma.

Learn more about Z-Score β†’

More Z-Score Examples

Example 1 easy

A student scored [formula] on an exam where the mean was [formula] and the standard deviation was [f

Example 3 easy

A data point has value [formula] in a distribution with [formula] and [formula]. Find its z-score.

Example 4 medium

In a class, test scores have mean [formula] and standard deviation [formula]. What raw score corresp

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