Alarge sleep study involving over 5000 american teenagers examined how many hours the participants slept on the weekend. the nightly sleep times were distinctly non-normal with a mean of 10 hours and a standard deviation of 2 hours. suppose we take a random sample of 100 nightly sleep times from this population. we can assume that the times in the sample are independent. what is the probability that the mean of these 100 (one hundreds hours)sleep times x¯x¯ is farther than 0.4 hours away from the population mean?

0.0228

Step-by-step explanation:

According to the central limit theorem even if the population distribution is non-normal, the distribution of randomly selected sample means is normal with the same mean of the population.

The question is then P(x>10.4) = 1-P(x<10.4) in the normal distribution of sample means where X is a sample mean higher than 10.4 hours.

z-score of 10.4 hour can be found using the formula:

z= where

Putting the numbers in the formula we get

z= = 2

Then the probability becomes

1-P(x<10.4) =  1-P(z<2) = 1-0.9772 =0.0228