Problem Solving

70, 75, 80, 85, 90, 105, 105, 130, 130, 130

the list shown consists of times, in seconds, that it took 10 schoolchildren to run a distance of 400 meters. if the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

answer choices:
1
2
3
4
5

answer: 3

Sum of all times: 1000
Mean of the 10 running times=100
1 standard deviation is 22.4 seconds, so the question asks you how many runners have a time which is superior to 122.4 seconds.
There are three times above (the three 130).

pepeprepa wrote: 1 standard deviation is 22.4 seconds, so the question asks you how many runners have a time which is superior to 122.4 seconds.

How 122.4 is "1 standard deviation below the mean"?
Isn't it "22.4 below the 100", which is 77.6?
Could you explain please?

I suck in word problems! so, Sorry!
Cheers,

Sorry for this concentration error, you are right.
We have 2 now

My answer is also 2. The times sum to 1000 w/ a mean of 100

100 - 22.4 = 77.6 anything below that is more than 1 standard deviation below the mean.

"how many of the 10 running times are more than 1 standard deviation below the mean"

Mean = 100, Standard Deviation = 22.4
1 standard deviation could be = 100 - 22.4 = 77.6 or 100 + 22.4 = 122.4
now the other part asks for more than 1 standard deviation - the items would be 80, 85, and 90. (more than 77.6)

other standard deviation 122.4 - items more than standard deviation - 130, 130, 130

answer would be 3 because 130 is more than the mean and 80, 85 and 90 are less than the mean but more than the standard deviation.

Hope this is clear.

AleksandrM wrote:My answer is also 2. The times sum to 1000 w/ a mean of 100

100 - 22.4 = 77.6 anything below that is more than 1 standard deviation below the mean.

mehravikas wrote:"how many of the 10 running times are more than 1 standard deviation below the mean"

Mean = 100, Standard Deviation = 22.4
1 standard deviation could be = 100 - 22.4 = 77.6 or 100 + 22.4 = 122.4
now the other part asks for more than 1 standard deviation - the items would be 80, 85, and 90. (more than 77.6)

The question is more than 1 std dev and less than the mean. std dev range is 77.6 to 122.4 so any numbers between this range falls under 1 std deviation so 80, 85 and 90 are under 1 std deviation. where as 70 and 75 are more than 1 std deviation and also less than mean so the ans has to be 2 numbers

Sorry anju but I am not convinced. Can we have the official answer please?

anju wrote:

mehravikas wrote:"how many of the 10 running times are more than 1 standard deviation below the mean"

Mean = 100, Standard Deviation = 22.4
1 standard deviation could be = 100 - 22.4 = 77.6 or 100 + 22.4 = 122.4
now the other part asks for more than 1 standard deviation - the items would be 80, 85, and 90. (more than 77.6)

The question is more than 1 std dev and less than the mean. std dev range is 77.6 to 122.4 so any numbers between this range falls under 1 std deviation so 80, 85 and 90 are under 1 std deviation. where as 70 and 75 are more than 1 std deviation and also less than mean so the ans has to be 2 numbers

The answer is 2.

Are more than 1 standard deviation below the mean of the 10 running times.

This mean what is number of running time are below 1st SD below the mean.

mean =100
1SD below the mean = 77.6

number of running times < 77.6

75, and 70.

Hope this helps.

If the answer is 2.

Then I think there is a problem in the way question is phrased. "more than 1 standard deviation below the mean"

parallel_chase wrote:The answer is 2.

Are more than 1 standard deviation below the mean of the 10 running times.

This mean what is number of running time are below 1st SD below the mean.

mean =100
1SD below the mean = 77.6

number of running times < 77.6

75, and 70.

Hope this helps.

mehravikas wrote:If the answer is 2.

Then I think there is a problem in the way question is phrased. "more than 1 standard deviation below the mean"

parallel_chase wrote:The answer is 2.

Are more than 1 standard deviation below the mean of the 10 running times.

This mean what is number of running time are below 1st SD below the mean.

mean =100
1SD below the mean = 77.6

number of running times < 77.6

75, and 70.

Hope this helps.

There is nothing wrong with the answer. One standard deviation below the mean is at 77.6 (100-22.4). Now, the question is asking "how many of the 10 running times are more than 1 standard deviation below the mean", which means how many timings are there between 77.6secs & 100 secs. There are 3 of them 80, 85 & 90.

Hope this helps.

I’m not sure but…
“how many of the 10 running times are more than 1 standard deviation below the mean’ sound ambiguous

For example, if 1 standard deviation below the mean is 10, then 2 standard deviation is 20; if you are asked about a number that are in the range of more than 1 standard deviation, you can chose a number between 10 and 20.

But the question, should said:

“how many of the 10 running times are between 1 standard deviation which is below the mean and the mean”

the answer is 3 for me as well.

Try and rephase the question with numbers in it.

The questions states

how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

You know that 1 standard deviation = 22.4 seconds. Therefore the question is

how many of the 10 running times are more than 22.4 seconds below the mean of the 10 running times?

You have also calculated that the mean of the ten running times = 100 seconds. Now the question becomes

how many of the 10 running times are more than 22.4 seconds below 100 seconds?

You could rephrase the question again replacing "below" with "less than", if you wanted. Then it becomes

how many of the 10 running times are more than 22.4 seconds less than 100 seconds?

Now we know, obviously, that 22.4 seconds less than 100 seconds = 77.6 seconds. Write

how many of the 10 running times are less than 77.6 seconds?

Make more sense now?

the mean is 100 and the standard deviation is 22.4
more than 1 standard deviation below the mean = numbers less than 77.6
there are only 2