Answer to Question #320017 in Statistics and Probability for Mirylle Anne

Question

The finished inside the diameter of a piston ring is normally distributed with a mean of 10 cm and a standard deviation of 0.03 cm.

a) what proportion of rings will have inside diameters exceeding 10.075 cm?

b) what is the probability that a piston ring will have an inside diameter between 9.97 and 10.03 cm?

c) below what value of inside diameter will 15% of the piston rings fall?

Answer 1

z=(x-$\mu)/\sigma$

a)

x=10.075

s=0.03

$\mu$=10

P(X>10.075)=1-P(z<=(10.075-10)/0.03)

=1-P(z=2.5)

=1-0.9938

=0.0062

b)

P(x1<x<x2)=P(9.97<x<10.03)

Z1=(9.97-10)/0.03 =-1

Z2=(10.03-10)/0.03=1

P(z1<x<z2)=P(z2=1)-P(z2=-1)

=0.8413-0.1587

=0.6826

c)

The corresponding z value for 0.15 is -1.04

z=(x-$\mu)/s$

z=-1.04

x=?

$\mu$=10

s =0.03

-1.04=(x-10)/0.03

x=9.97