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 in diameter and that 40 percent of the screws are grater than 1.71 inches in diameter. What is the mean diameter of screws produced by this machine? what is the standard deviation of the screws produced by the 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
Learn more:
Assume that adults have iq scores that are normally distributed with ...
brainly.in/question/11133397
The mean length of mature whiting is 35 cm and the standard ...
brainly.in/question/13450142
The value of the cumulative standardized normal distribution at z is ...
brainly.in/question/11376268
The diameter of screws produced
https://brainly.in/question/18140953