Heights of males are normally distributed with the mean 170 cm and the standard deviation of 8 cm. What is the probability that males are shorter than 176 cm?

Answer 1

To find the probability that males are shorter than 176 cm, we first need to standardize the height using the z-score formula:

z = (x - μ) / σ

Where:
x = height (176 cm)
μ = mean (170 cm)
σ = standard deviation (8 cm)

z = (176 - 170) / 8
z = 0.75

Next, we look up the z-score of 0.75 in the standard normal distribution table to find the corresponding probability. From the table, we find that the probability of z being less than 0.75 is approximately 0.7734.

Therefore, the probability that males are shorter than 176 cm is approximately 0.7734 or 77.34%.