Answer:
a) Atleast 75%
b) Atleast 88.9%
c) 95%
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 6.7
Standard Deviation, σ = 1.6
Chebyshev's Theorem:
- Atleast
percent of data lies within k standard deviation of mean.
Empirical Rule:
- Almost all the data lies within 3 standard deviation for a normal data.
- Around 68% of data lies within 1 standard deviation of mean.
- Around 95% of data lies within 2 standard deviation of mean.
- Around 99.7% of data lies within 3 standard deviations o mean.
a) minimum percentage of individuals who sleep between 3.5 and 9.9 hours
We have to find the percent of data lying within 2 standard deviation of mean.
Putting k = 2
Atleast 75% of of individuals who sleep between 3.5 and 9.9 hours.
b) minimum percentage of individuals who sleep between 2.7 and 10.7 hours
We have to find the percent of data lying within 3 standard deviation of mean.
Putting k = 3
Atleast 88.9% of of individuals who sleep between 2.7 and 10.7 hours.
c) percentage of individuals who sleep between 3.5 and 9.9 hours per day.
Thus, we have to find the percentage of data lying within 2 standard deviation.
By empirical rule, around 95% of data lies within 2 standard deviation.
Thus, 95% of of individuals who sleep between 3.5 and 9.9 hours.
This is higher than the percentage obtained from Chebyshev's rule.