Question

Steel rods are manufactured with a mean length of 28 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm.

• If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 27.9 cm and 28.1 cm?
• If an order comes in for 25,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 27.9 cm and 28.05 cm?

Answer 1

Solution :

Given that ,

mean = = 28

standard deviation = = 0.06

(a)

P(27.9 < x < 28.1) = P((27.9 - 28)/ 0.06) < (x - ) /  < (28.1 - 28) / 0.06) )

= P(-1.67 < z < 1.67)

= P(z < 1.67) - P(z < -1.67)

= 0.9525 - 0.0475

= 0.905

rods = 10000 * 0.905 = 9050 are expect .

(b)

P(27.9 < x < 28.05) = P((27.9 - 28)/ 0.06) < (x - ) /  < (28.05 - 28) / 0.06) )

= P(-1.67 < z < 0.83)

= P(z < 0.83) - P(z < -1.67)

= 0.7967 - 0.0475

= 0.7492

Rods = 0.7492 * 25000 = 18730 are expect .