Question

Automated manufacturing operations are quite precise but still vary, often with distribution that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N(1,0.001)N(1,0.001) distribution. The specifications allow slot widths between 0.999750.99975 and 1.000251.00025. What proportion of slots meet these specifications

Answer 1

The answer is "15.85%"

Explanation:

The complete question is defined in the attachment file please find it.

Given:

`\mu = 1\\\\\sigma = 0.001 \\\\`

Converting the Standard Normal:

`\to P(X < x) = P( Z < (( X - \mu ))/(\sigma) )\\\\\to P ( 0.9998 < X < 1.0002 ) = P ( Z < (( 1.0002 - 1 ))/(0.001)) - P ( Z < (( 0.9998 - 1 ))/(0.001))\\\\`

`= P ( Z < 0.2) - P ( Z < -0.2 )\\\\= 0.5793 - 0.4207\\\\= 0.1585\\\\= 15.85\%\\\\`