Question

Heights of adult women in the united states are normally distributed with a population mean of μ = 63.5 inches and a population standard deviation of σ = 2.5. a medical researcher is planning to select a large random sample of adult women to participate in a future study. what is the standard value, or z-value, for an adult woman who has a height of 50.4 inches? (calculate to 1 decimal)

Answer 1

Given:
population mean of μ = 63.5 inches
population standard deviation of σ = 2.5 inches
adult woman who has a height of 50.4 inches

z = (x – μ) / σ

z = (50.4 - 63.5) / 2.5 = -13.1 / 2.5 = -5.24 

The z-value of an adult woman who has a height of 50.4 inches is -5.24 or -5.24 standard deviation below the mean.