Question

In a survey of first graders, their mean height was 49.9 inches with a standard deviation of 3.15 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?

Answer 1

Height = 47.77 inches

Explanation:

We are given;

Mean = 49.9 in

Standard deviation;SD = 3.15 in

The first quartile is the 25th percentile, which means it's where 25% of the data falls.

Now from the normal distribution table attached, we can see that the z-value for 25% or 0.25 is approximately

-0.675.

To find the height that represents the first quartile of these students, we will use the formula;

z = (height - mean)/(SD)

Making height the subject ;

height = (z × SD) + mean

Plugging in the relevant values to obtain;

Height = (-0.675 × 3.15) + 49.9

Height ≈ 47.77 inches