z = (x-mu)/sigmaIf the z-score is known and the value of x is needed, solving the previous equation for x gives
x = mu + z * sigmaThis simply states that x is z standard deviations above the mean.
Ridge counts in finger prints are approximately normally distributed with a mean mu = 140 and standard deviation sigma = 50.
Find the probability that an individual chosen randomly has a ridge count:
Always draw a sketch.
(1) The area to the right of 200 under the given normal curve is equal to the area to the right of
z = (200 - 140)/50 = 1.20under the standard normal curve. The area to the left of 1.20 is .8849 from the table, so the answer is 1 - .8849 = .1151.
(2) The area to the left of 100 under the given normal curve is equal to the area to the left of
z = (100 - 140) / 50 = -0.80under the standard normal curve. This area is .2119 from the table.
(3) The area between 100 and 200 under the given normal curve is equal to the area between -0.80 and 1.20 under the standard normal curve. From the above solutions, this is .8849 - .2119 = .6730.
Bret Larget, email@example.com