If the measurements of the radius of a piston are normally distributed with a mean of 1.85 inches and a standard deviation of 0.25 inches, determine the probability that the radius of a piston randomly chosen from a production assembly line has a radius between 1.7 and 2.1 inches.
Question 4 options:
a) 2.67%
b) 56.7%
c) 15.83%
d) 11.56%

Question

If the measurements of the radius of a piston are normally distributed with a mean of 1.85 inches and a standard deviation of 0.25 inches, determine the probability that the radius of a piston randomly chosen from a production assembly line has a radius between 1.7 and 2.1 inches.
Question 4 options:
	a)	2.67%
	b)	56.7%
	c)	15.83%
	d)	11.56%

daenio · Answer

@lalaly 
@blockcolder 
@ash2326 
@ZhangYan

blockcolder · Answer

The z-score of 1.7 is (1.7-1.85)/0.25=-0.6 while the z-score of 2.1 is (2.1-1.85)/0.25=1.
The probability that the data is to the left of 1.7 is -0.6 is 0.2743 while the probability that the data is to the left of 2.1 is 0.8413. (Consult a table for this.) Thus, the probability that the data is between the two is 0.8413-0.2743=0.567=56.7%.

daenio · Answer

Thank you!