A set of college student heights are normally distributed with a mean of 170.4 centimeters and a standard deviation of 10 centimeters.

Question

What proportion of student heights are between 170.5 centimeters and 180.3 centimeters?

Answer 1

Use 2 different z-scores to find the proportions of heights between 170.5 and 180.3 cm.

z = (170.5 - 170.4) / 10 = 0.1/10 = 0.01

z = (180.3 - 170.4) / 10 = 0.9/10 = 0.09

P(z < 0.09) - P(z < 0.01) = 0.5359 - 0.5040 = 0.0319

The proportion of student heights that are between 170.5 and 180.3 cm is 0.0319.