The U.S. Weather Bureau has provided the following inforÂmation about
The U.S. Weather Bureau has provided the following information about the total annual
number of reported tornados in the United States for the years 1956 to 1975:
856 926
564 660
604 608
616
653
697 888
657 741
464 1102
704 947
906 918
(a) Use a calculator with mean and standard deviation keys to verify that the mean number of tornados per year is 730, with a sample standard deviation of 172 tornados.
(b) Use Chebyshev's theorem to find an interval centered about the mean for the annual number of tornados in which you would expect at least 75% of the years to fall.
(c) Use Chebyshev's theorem to find an interval centered about the mean in which
you would expect at least 88.9% of the years to fall.
Solution: (a) We have that
Using EXCEL we get that the standard deviation is 172.1783, which is approximated to 172.
(b) By Chebyshev’s theorem we know that
Therefore, we are looking for asuch that
which means that, so we take . Then, the interval we are looking for is
(c) Following the same rationale, we need such that
which means that, so we take . Then, the interval we are looking for is