The diameter of screws produced by a particular machine is normally distributed. Based on past experience, it is known that 30 percent of the screws are less than 1.30 inches’ diameter and that 40 percent are greater than 1.71 inches’ diameter of the screws.
What is the mean diameter of the screws produced by this machine?
What is the standard deviation of the diameter of the screws produced by this machine?
Answers
Given : 30 percent of the screws are
less than 1.30 inches in diameter and that 40 percent of the screws are greater than
1.71 inches in diameter.
To find : mean diameter of screws produced by this machine
standard deviation of the diameter of the screws produced by this machine
Solution:
Z score = ( Value - Mean)/SD
30 percent of the screws are less than 1.30 inches
Z score for 30 % = -0.525
=> -0.525 = ( 1.3 - Mean)/SD
=> -0.525SD = 1.3 - Mean
=> Mean = 1.3 + 0.525SD
40 percent of the screws are greater than
1.71 inches
=> 60 % screws are less than 1.71 inches
Z score for 60 % = 0.253
0.253 = (1.71 - Mean)/SD
=> 0.253SD = 1.71 - mean
=> Mean = 1.71 - 0.253SD
Equating mean
1.3 + 0.525SD = 1.71 - 0.253SD
=> 0.778SD = 0.41
=> SD = 0.527
Mean = 1.3 + 0.525SD = 1.3 + 0.525 *
0.527 = 1.577
mean diameter of screws produced by this machine = 1.577 inch
standard deviation of the diameter of the screws produced by this machine
= 0.527 inch
Answer:
0.527 inch is the correct answer