Normal Distribution - Find Mean and Stadard Deviation

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In a marathon, Over 10,000 runners competed . The time of the runners follow a normal distribution. Only 16% of runners were able to finish in less than 3 hr 43 min 31 sec. 97.5% of the runners needed at least 2 hr 54 min 54 sec to complete. Determine the mean and the standard deviation.

May 11th, 2015

we set up 2 equations

16% = 1 standard deviation and more LESS than the mean. So,

3hr43min31secs - mean / standard deviation SD = - 1

97.5% = 2 standard deviations and less GREATER than the mean, So,

2hr54min54sec - mean / SD = -2

Convert minute and secs to hours, giving us  3.725 hrs and 2.915 hours

then,

3.725 - mean / SD = -1

and

2.915 - mean / SD = -2

Subtracting second equation from first cancels mean, and gives

SD = 0.81 hours

Then the mean is 3.725 + 0.81 = 4.535 hours or 4hours 32 minutes 6 seconds



May 11th, 2015

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May 11th, 2015
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