A machine produces steel rods. The lengths of the rods are normally distributed with a mean of 26 cm and a standard deviation 1 cm. Rods that are longer than 27 cm or shorter than 24 cm have to be discarded. The machine produces 500 rods per shift. How many rods per shift have to be discarded?
Answers
Given : A machine produces steel rods. The lengths of the rods are normally distributed with a mean of 26 cm and a standard deviation 1 cm. Rods that are longer than 27 cm or shorter than 24 cm have to be discarded. The machine produces 500 rods per shift.
To find : How many rods per shift have to be discarded?
Solution:
Mean = 26 cm
SD = 1 cm
Z = ( Value - Mean)/SD
27 cm
Z = (27 - 26)/1 = 1 => 0.8413
0.8413 of 500 = 420.65
24 cm
Z = (26 - 26)/1 = -2 => 0.0.0228
0.0228 of 500 = 11.4
Correct pieces between 24 cm & 27 cm
= 420.65 - 11.4
= 409.25
Pieces to be rejected = 500 - 409.25 = 90.75
91 pieces to be discarded every shift
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