Interpreting Z-Scores (Page 3 of 4) in pdf

Interpreting Z-Scores Page 3

STA 2e: Sect. 3.2 Worksheet #2

Name __________________________

ORMAL

ISTRIBUTIONS

FINDING A PERCENT/PROPORTION given an x value

FINDING AN X VALUE given a percentage/proportion

Look in the body of Table A for the entry closest to the

Standardize x t o restate the problem in terms of a

given proportion or the proportion to the left of given

standard Normal variable z. Draw a picture to show the

proportion to find the corresponding z. “Unstandardize”

area of interest under the standard Normal curve.

to transform the solution from a z-‐score to a value of x

Then find the required area under the standard Normal

−

curve using Table A.

using the equation

Scores on the Wechsler Adult Intelligence Scale, a standard IQ test, are approximately normal for the 20

to 34 age group with µ = 110 and σ = 25.

What percent of this age group have an IQ less than 100?

What percent of this age group have an IQ between 90 and115?

Find the 80th percentile of the IQ scores distribution of 20 to 34 year olds.

Find the IQ score which separates the lowest 25% of all IQ scores for this age group

from the highest 75%.

The adult men of the Dinaric Alps have the highest average height of all regions. The distribution of

height is approximately normal with a mean height of 6 ft 1 in (73 inches) and

standard deviation of 3 inches.

Find the 40th percentile of the height of Dinaric Alps distribution for men.

What percentage of men have a height greater than 74 inches?

Interpreting Z-Scores Page 3