SOLUTION: The amount of money spent by tourists when visiting Istanbul Modern is normally distributed with a standard deviation of 100$ and mean 1000$. If it is known by the authorities tha

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Question 1185817: The amount of money spent by tourists when visiting Istanbul Modern is normally distributed with a standard deviation of 100$ and mean 1000$. If it is known by the authorities that 50 % of the tourists spend within the range of mean ±d. find the value of d.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you are looking for the area under the normal distribution curve that is equal to .5 and equidistant from the mean, i.e. the low score is the same distance from the mean as the high score.

the area to the left of the mean is equal to .5
you want half of that area to the left and half of that area to the right.
that means the area to the left of your low score is .25 and the area to the left of your high score is .75, because .75 minus .25 = .5

the following calculator lets you do this directly.

https://davidmlane.com/hyperstat/z_table.html

the results of using that calculator are shown below:



your low score would be 932.551
your high score would be 1067.449

d would be equal to 1000 minus 932.551 = 67.449
d would also be equal to 1067.449 minus 1000 = 67.449.

you could also have gotten the same values by finding the score that had .25 area to the left of it and the score that had .75 area to the left of it.

the area in between would be .75 minus .25 = .50.

it would be the same scores, as shown below: