Question

A computer numeric controlled (CNC) machine is used to create a part for a medical device. The sizes of the manufactured parts are normally distributed, with a mean with of 2.00 inches and a standard deviation of 0.005 inches. The parts are only useable when their widths are between 1.99 and 2.01 inches. What proportion of parts are useable?

HINT: use the NORM.DIST function twice.

a	0.93
b	0.95
c	0.98
d	0.99

Answer 1

Solution :

Given that ,

mean = = 2.00

standard deviation = = 0.005

P(1.99 < x < 2.01) = P[(1.99 - 2.00)/ 0.005 ) < (x - ) /  < (2.01 - 2.00) / 0.005 ) ]

= P(-2.0 < z < 2.0)

= P(z < 2.0) - P(z < -2.0)

Using z table,

= 0.9772 - 0.0228

= 0.9544

= The proportion is = 0.95

correct option is = b