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The U.S. Weather Bureau has provided the following informati

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The U.S. Weather Bureau has provided the following informati [#permalink] New post   31 Jul 2020, 10:17
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The U.S. Weather Bureau has provided the following information about the total annual number of reported tornadoes in the United States for the years 1956 to 1975:

505 856 564 604 616 697 657 464 704 906

585 926 660 608 653 888 741 1,102 947 918

The average number of tornadoes per reported year is 730, and the standard deviation of the set is 168. If one of the numbers in the data set is chosen at random, what is the probability that the number is less than the median and is not within one standard deviation of the mean?

A. 10%

B. 15%

C. 25%

D. 30%

E. 40%
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A
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chacinluis
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The U.S. Weather Bureau has provided the following informati [#permalink] New post   Updated on: 03 Dec 2021, 15:10
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Mean=730
Standard Deviation=168

The fast way of solving this question is using
Fact: The median is always within one standard deviation away from the mean

Using this fact then

730-168=562
730+168=898
So the median is between 562 and 898 inclusive
And numbers beyond one standard deviation away from the mean are those below 562 and above 898

Condition1: number must be below the median
Condition2: number must be beyond one standard deviation away from the mean

Both conditions combine to give us numbers below 562.
464 and 505 are the only numbers satisfying this

We also have 20 numbers in the set.

Answer is 2/20=1/10=0.1

Final Answer: 10%

Originally posted by chacinluis on 03 Aug 2020, 03:30.
Last edited by chacinluis on 03 Dec 2021, 15:10, edited 1 time in total.
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Re: The U.S. Weather Bureau has provided the following informati [#permalink] New post   01 Aug 2020, 22:40
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Since median will be greater than (730 - 168 = 562) ie. the one standard deviation less than mean. So all you have to do is see the probability of selecting number less than 562.
There are only two numbers less than 562 (505 and 464) and total numbers are 20. Therefore,

2/20 * 100 = 10%.
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Re: The U.S. Weather Bureau has provided the following informati [#permalink] New post   02 Aug 2020, 00:32
Any other explanation?
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Re: The U.S. Weather Bureau has provided the following informati [#permalink] New post   19 Aug 2021, 21:39
Isnt the median here , the median of two numbers? Or am i wrong?
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Re: The U.S. Weather Bureau has provided the following informati [#permalink] New post   20 Aug 2021, 02:09
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Explanation:

To find the mean, let us first arrange these 20 terms in ascending order:
464, 505, 564, 585, 604, 608, 616, 653, 657, 660, 697, 704, 741, 856, 888, 906, 918, 926, 947, 1102

Median (for even number of terms) = \(\frac{10^{th} term + 11^{th} term}{2} = \frac{660 + 697}{2} = 678.5\)

Average (given) = 730
SD (given) = 168
1SD of mean means 1SD above or 1SD below mean i.e. (730 - 168) to (730 + 168) = 562 to 898

Find the numbers which are less than the median;
464, 505, 564, 585, 604, 608, 616, 653, 657, 660

Which are not within one standard deviation of the mean;
464, 505, 564, 585, 604, 608, 616, 653, 657, 660

Required probability = \(\frac{2}{20} (100) = 10\)%
Hence, option A
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Re: The U.S. Weather Bureau has provided the following informati [#permalink] New post   16 Mar 2023, 11:57
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Re: The U.S. Weather Bureau has provided the following informati [#permalink]
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