So, I know this question has been asked on here before but Ive read the explanations and still have not understood. I'm trying to teach myself this process because I do online math. However, math does not come easily to me so its been pretty difficult. Any help from anybody on the process of solving this problem would be greatly greatly appreciated. Thanks so much. :)
1.) The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the probability that a student will finish the test in less than 70 minutes?
Stacey Warren - Expert brainly.com
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its an empirical rule assessment
what do you know about the empirical rule?
the empirical rule is an approximation of a normal standard probability curve
within +- 1 standard deviation from the mean, there lies about 68% of the data
within +- 2 standard deviation from the mean, there lies about 95% of the data
within +- 3 standard deviation from the mean, there lies about 99% of the data
with a mean of 60, and a standard deviation of 10; 70 is +1 standard deviations away from the mean: 60+10 = 70
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all the values less then 70 is what we want to find .... we should know that anything up to the mean equates to 50% of the normal distribution, so all thats left is to add in the missing percentage
since \(\pm1\) sd gives us 68% of the data is split about the mean; 68/2 = 34 left unaccounted for.
50% + 34% should account for approximately the whole area we seek
Wow, Ok thank you so much for all you just wrote. I understand all the way up to the bell curve that you drew. So the entire area from 50 to 70 is 68%? And why did you divide by 2?
im only missing half the area around the mean .... from 60 to 70
(50 to 60) + (60 to 70) = 68%
but, (50 to 60) is equal to (60 to 70)
2(60 to 70) = 68%
(60 to 70) = 68/2 %
we know the area from say: -infinity to 60 is 50% of the data; all thats missing is the part from (60 to 70) to account for
Ok, so I think I understand. So I need to divide 68% by 2... so is the answer 34%?
or would it be 34% plus something..
34% is the part that missing.
we know of 50%, and then by filling in the missing part with the 34% we get the required approximation.|dw:1378243701319:dw|
so 34% plus 50%?
so the answer is 84%?
that would be the approximation yes. And unless they want a more accurate assessment, I would say thats it
.8413 is what i get for something more accurate using a normalcdf function on my ti83
Ok, well either way thank you SO MUCH for helping me. You have no idea how appreciative I am, honestly. This was driving me crazy I was trying to figure this out for days, haha. Thank you, thank you, thank you!