mean time taken to solve prob (need help w/ starting)

Standard deviation, mean, variance, z-scores, t-tests, etc.
zorro
Posts: 28
Joined: Sat Jun 12, 2010 9:26 am
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mean time taken to solve prob (need help w/ starting)

Question :
The mean time taken by 500 students to solve a problem is 151 sec and the standard deviation is 15 sec . Assuming that the times are normally distributed , find how many students take
i) between 120 and 155 sec.
ii) more than 185 sec.
Solution :

n = 500
$\bar{X}$ = 151
s = 15

i) between 120 and 155 sec
$z = \frac{120 - 151}{15/ \sqrt{500}} = -9.773$ (is this correct ?)

(kindly just tell me which formula to use so that i can get started )

bobbym
Posts: 2
Joined: Mon Mar 21, 2011 11:47 am
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Re: mean time taken to solve prob (need help w/ starting)

Hi zorro;

i) 120 to 154 represents -2.06666 sd below the mean and .26666 sd above the mean. The area under the curve that represents the standard normal curve is:

$\Large \int_{-2.0666}^{0.2666} \ \frac{e^{-\frac{x^2}{2}}}{\sqrt{2 \pi }} \, dx \approx \ .5857$

Meaning that 58.57% of the students fall into this range.

$.5857 \cdot 500 = 292.86$

So 292.86 students take between 120 and 155 seconds.

ii) 185 is 2.2666 sd above the mean. This represents .0117 or 1.17 % of the students.