Question

1. The distribution of heights of adult women is Normally distributed, with a mean of 65 inches and a standard deviation of 3.5 inches.Susan's height has a z-score of negative 0.5 when compared to all adult women in this distribution. What does this z-score tell us about how Susan's height compares to other adult women in terms of height?

Answer 1

A z-score is the number of standard deviations from the mean value of the reference population

The z-score in the center of the curve is zero. The z-scores to the right of the mean are positive and the z-scores to the left of the mean are negative. If you look up the score in the z-table, you can tell what percentage of the population is above or below your score.

Given

mean= 65 inches

standard deviation = 3.5 inches

Z- score = - 0.5

The z score tells you how many standard deviations from the mean your score is.

So, the z score = - 0.5 tells -0.5 standard deviations below the mean.

And

From Z- table

  

i.e., 30.85%

This tells us that the percentage of adult women whose height is less than the Susan's height is 30.85%

i.e., 30.85% of the adult women are less than the Susan's height.

or

100-30.85= 69.15%

69.15% of the adult women are greater than Susan's height.