Question

Quiz: Chapter 3 Review Quiz 2 of 12 (1 At one (a) What (b) What th-the that we within 2 5 standard deviations of the mean? Round to the nearest hundredth as needod ) (Round to the nearest handredth as needed) The gasoline prices that are within 2 5 standard deviations of the mean are to (Use ascending order) (c) %isthemiinum percentage of gasoine stations that had prices between SJ 3, and S O Type here to search

Answer 1

We know by Chebyshev's inequality we know that  at least $1-{1\over k^2}$ of the distribution's values are within $k$ standard deviations of the mean

a) Here k=4, so $1-{1\over 4^2}=0.9375$

So 93.75%

b) Here k=2.5 , so $1-{1\over (2.5)^2}=0.84$

So 84.00 % prices within 2.5 standard deviation from the mean

As $3.49-2.5\times 0.06=3.34$ and $3.49+2.5\times 0.06=3.64$

c) Since $3.49-2\times 0.06=3.37$ and $3.49+2\times 0.06=3.61$

So 3.37 to 3.61 prices lies within 2 standard deviations from the mean

Hence the percentage of data is $1-{1\over 2^2}=0.75$

So 75.00 % data lies within 3.37 to 3.61