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The U.S. Weather Bureau has provided the following informati
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31 Jul 2020, 10:17
31 Jul 2020, 10:17
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51% (03:14) correct
48% (02:34) wrong based on 54 sessions
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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%
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%
The U.S. Weather Bureau has provided the following informati
[#permalink]
Updated on: 03 Dec 2021, 15:10
Updated on: 03 Dec 2021, 15:10
6
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%
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.
Last edited by chacinluis on 03 Dec 2021, 15:10, edited 1 time in total.
General Discussion
Re: The U.S. Weather Bureau has provided the following informati
[#permalink]
01 Aug 2020, 22:40
01 Aug 2020, 22:40
1
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%.
There are only two numbers less than 562 (505 and 464) and total numbers are 20. Therefore,
2/20 * 100 = 10%.
