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?
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%.