Expert: statmaster - 8/16/2009

Question
Suppose that the size of malignant breast lesions as observed on mammograms approximately follows a normal distribution with mean of 12 mm and standard deviation of 6 mm. What is the probability that a malignant lesion will be larger than 10mm?

Answer
Let the size of malignant breast lesions as observed on mammograms approximately follows a normal distribution with mean of 12 mm and standard deviation of 6 mm. To find the probability that a malignant lesion will be larger than 10mm

=P(x>10)
=P(x-mean/sd> 10-12/6)   by defn z=x-mean/Sd
=P(Z>-0.3333)

By excel function we can find as  =NORMDIST(10,12,6,TRUE) where x=10, mean =12,sd=6,TRUE
P(Z>-0.3333)=1- NORMDIST(10,12,6,TRUE)
           =1-0.3694
=0.6306