Question

You are compiling 3D reconstructions from 2D x-ray images obtained from a medical scanner. An average 2D x-ray image occupies 3.5 megabytes of memory with a standard deviation of 1.6 megabytes. If your initial reconstruction will be compiled from 64 x-ray images, find the probability that the average 2D image size in your reconstruction is (a) at most 3.0 megabytes; (b) more than 3.8 megabytes

Answer 1

Solution :

Given that ,

mean = = 3.5

standard deviation = = 1.6

(a)

P(x 3.0)

= P[(x - ) / (3.0 - 3.5) / 1.6]

= P(z -0.31)

= 0.3783

Probability = 0.3783

(b)

P(x > 3.8) = 1 - P(x < 3.8)

= 1 - P[(x - ) / < (3.8 - 3.5) / 1.6)

= 1 - P(z < 0.19)

= 1 - 0.5753

= 0.4247

Probability = 0.4247