Question

A data set has a mean of 42 and a standard deviation of 7.8 if an element in the set is 54 find its z-score

Answer 1

Answer:

The z-score is 1.54

Step-by-step explanation:

Given:

x = 54

μ = 42

σ = 7.8

Required:

Z-score

Equation:

$Z\: =\: \frac{x\:-\:μ}{σ}$

where: Z - standard score

x - value

μ - mean

σ - standard deviation

Solution:

Substitute the value of x, μ and σ

$Z\: =\: \frac{x\:-\:μ}{σ}$

$Z\: =\: \frac{54\:-\:42}{7.8}$

$Z\: =\: 1.54$

Final Answer:

The z-score is 1.54