The mean of a set of data is 108.06

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 309 People

The mean of a set of data is 108.06 and its standard deviation is 115.45. Find the z score for a value of 489.67. Round to two decimal places as needed.

Answered by maham237 @ 13/01/2021

Answer:

The z-score for the value 489.67 is 3.31.

Step-by-step explanation:

If X $\sim$ N (µ, σ²), then $Z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z $\sim$ N (0, 1).

The distribution of these z-variate is known as the standard normal distribution.

The information provided is:

μ = 108.06

σ = 115.45

Compute the z-score for the raw score X = 489.67 as follows:

$Z=\frac{X-\mu}{\sigma}=\frac{489.67-108.06}{115.45}=3.3054\approx3.31$

Thus, the z-score for the value 489.67 is 3.31.

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