According to the Sleep Foundation, the average night’s sleep is 6.8 hours. Assume the standard deviation is .6 hours and that the probability distribution is normal.What is the probability that a randomly selected person sleeps 6 hours or less? g

9.18% probability that a randomly selected person sleeps 6 hours or less

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the probability that a randomly selected person sleeps 6 hours or less?

This is the pvalue of Z when X = 6. So

has a pvalue of 0.0918

9.18% probability that a randomly selected person sleeps 6 hours or less

8/9

Step-by-step explanation: