Z-Score Math Example 4

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

Example 4

medium
In a class, test scores have mean 7070 and standard deviation 88. What raw score corresponds to a z-score of 1.251.25?

Solution

  1. 1
    Use the relationship x=ฮผ+zฯƒx = \mu + z\sigma.
  2. 2
    Substitute: x=70+1.25(8)x = 70 + 1.25(8).
  3. 3
    Compute: 1.25ร—8=101.25 \times 8 = 10, so x=80x = 80.

Answer

x=80x = 80
A z-score tells how many standard deviations a value lies above or below the mean. To recover the original score, multiply by the standard deviation and shift by the mean.

About Z-Score

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

Learn more about Z-Score โ†’

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 2 medium

On Test A, Maria scored [formula] ([formula], [formula]). On Test B, she scored [formula] ([formula]

Example 3 easy

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

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