Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 7.45, \sigma = 0.65[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 7.45}{0.65}[/tex]
[tex]X - 7.45 = 0.65*2.327[/tex]
[tex]X = 8.96[/tex]
At least 8.96 hours of sleep to be in the top 1%.
Answer:
2.31
.12
7.73
Step-by-step explanation:
σx¯=0.653–√0=0.12
By plugging all the numbers into the formula z=x¯−μσx¯ we find that
2.31=x¯−7.450.12
0.28=x¯−7.45
7.73=x¯
