The average height of adult females is 64.4 inches, with a standard deviation of 2.3 inches and a normal distribution. Rayna is 67.1 inches tall. What is the standardized score for Rayna’s height?

A. -1.17
B. 1.17
C. -0.17
D. 0.17
E. Unable to determine the standardized score

Question

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absor201 absor201 · Answer 1 · 2020-01-23T16:29:53+01:00

Option B: 1.17 is the correct answer

Step-by-step explanation:

First of all, lets define standard score.

"Standard score is the representation of a data value in terms of distance from standard deviation from the mean. It is also called z-score"

Given

Mean = μ = 64.4 inches

Standard Deviation = σ = 2.3 inches

We have to find the standard score for Rayna's height

So,

Let x = 67.1

the formula for z-score is:

[tex]z-score =\frac{x-mean}{SD}\\= \frac{67.1-64.4}{2.3}\\= \frac{2.7}{2.3}\\=1.1739[/tex]

Rounding off to nearest hundredth

z-score = 1.17

Hence,

Option B: 1.17 is the correct answer

Keywords: z-score, standard deviation

Learn more about z-score at:

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