# A machine is designed to produce parts having an average diameter of 2cm, and a standard deviation of 0.3 cm. If the distribution of the diameters of manufactured product is normal.

Question:

A machine is designed to produce parts having an average diameter of 2cm, and a standard deviation of 0.3 cm. If the distribution of the diameters of manufactured product is normal.

(a) What is the probability that a randomly selected part will have a diameter exceeding 2.05 cm?
(b) What is the probability that a randomly selected part will be between 1.95 cm and 2.05 cm?

Solution:

(a) The probability that a randomly selected product have diameter exceeding 2.05 cm is given by between x = 2.05 and + . This area can be determined by standardizing x:

It means there is 4.75% probability that diameter will exceed 2.05cm.

(b) The probability that selected product has diameter between 1.95cm and 2.05cm is given by the area between x 1 = 1.95 and x 2 = 2.05. This area can be determined by standardizing x 1 and x2 as z1 and z2

It means there is 90.50% probability that product has diameter between 1.95 cm and 2.05cm.