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:


504 585

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

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