Monday, November 16, 2009

Capacities of the cranial cavities?

if the capacities of the cranial cavities of a certain population are apprximately normally distributed with a mean of 1400cc and a standard deviation of 125, find the probability that a randomly selected person from the given population will have a cranial cavity capacity greater than 1450cc

Capacities of the cranial cavities?
Start with the equation for a Gaussian probability distribution (random distribution)

f(x) = {e^-[(x-u)^2] / 2s^2} / [s * (2*pi)^0.5]


x = the cranial capacity in cc

u = the mean of the sample (1400 cc)

s = standard deviation = 125

pi = 3.14159

1) Integrate this equation and find the area under the curve from -infinity to +infinity

Call this a1

2) integrate the equation from 1450 cc to +infinity

call this a2

The ratio of the answers from 2 and 1 equal the probability that the cranial capacity exceeds 1450

p = a2/a1

Hope this helps,


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