Answer:
At least 8.96 hours of sleep to be in the top 1%.
Step-by-step explanation:
When the distribution is normal, we use 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 question, we have that:
How many hours of sleep to be on the top 1%?
The top 1% is the 100 - 1 = 99th percentile, which is X when Z has a pvalue of 0.99. So X when Z = 2.327. Then
At least 8.96 hours of sleep to be in the top 1%.