Please using R studio, I wanna solve this question 2. Suppose that a data set ha

Question

Please using R studio, I wanna solve this question

2. Suppose that a data set has sample mean 5.5 and sample standard deviation 2.5. (1) If the data set roughly follows a normal distribution, please find an interval such that it is symmetric around the sample mearn and about 95% of data values fall within the interval. (2) If the data set follows an unknown distribution, please find an interval such that it is symmetric around the sample mean and at least 80% of data values fall within the interval

Explanation / Answer

Ans:

1)Using Empirical rule(as data has normal distribution),approximately 95% of the data falls within 2 standard deviations of the mean.

lower limit=5.5-2*2.5=0.5

upper limit=5.5+2*2.5=10.5

2)As,distribution is unknown,use cheybev's theorm.

Atleast 1-(1/k^2) of the data lies within k standard deviation of the mean.

1-(1/k^2)=0.8

(1/k^2)=0.2

k^2=5

k=2.236

lower limit=5.5-2.236*2.5=-0.09

upper limit=5.5+2.236*2.5=11.09

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