Page 28 - Quality control of pharmaceuticals (07-PA 704)

Example
Consider a normal distribution with µ = 20 and σ = 2. Determine the
probability that a measurement will be in the interval from 16 to 20.

z = = (16 - 20) / 2 = - 2

Thus y = 16 lies 2 standard deviations below µ = 20.
Ignoring the negative sign and referring to Table 1, we find the area
corresponding to z = 2 to be 0.4772. This is the probability that a
measurement falls in the interval from 16 to 20.

Example
Total yearly milk productions for cows in a herd are assumed to be

normally distributed with µ = 70 pounds and σ = 13 pounds. What is
the probability that the milk production for a cow chosen at random
will lie in the interval from 60 pounds to 90 pounds? What is the
probability that the milk production for the randomly selected cow
will exceed 90 pounds in a given year?

z = (60 - 70) / 13 = - 0.77
Referring to Table 1, the area between y = 60 and µ = 70 is 0.2794.
z = (90 - 70) / 13 = 1.54
Referring to Table 1, the area between 70 and 90 is 0.4382.