Question

The students of a large university in Luzon were studied regarding their hours of sleep at night. The hours of sleep can be modeled as a normal distribution with mean of 6.9 hours and standard deviation of 1.5 hours. Find the 85th percentile of the distribution for hours of sleep.

Answer 1

As the distribution of the hours of sleep can be modeled as normal distribution with mean $\mu$ of 6.9 hours and standard deviation $\sigma$ of 1.5 hours.

Using the tables of the percentiles of the standard normal distribution, we have that 85th percentile of this distribution corresponds to 1.0364.

This means that 85th percentile of normal distribution with mean $\mu$ of 6.9 hours and standard deviation $\sigma$ of 1.5 hours will be

$x_{85\%} = \mu +1.0364\sigma = 6.9+1.0364\cdot 1.5 = 8.4546\approx8.5$ hours.

Answer. 85% of students sleep at night less than 8.5 hours.