Question

Put a lid on it! The supplier is considering two changes to reduce to 1% the

Answer 1

Answer:

A) 3.996 inches

B) 0.01

C) option B

Step-by-step explanation:

Note: The diameter of the lid is between : 3.95 and  4.05

A) calculate the supplier set mean diameter

std = 0.02 inch

P( x < 3.95 ) = 1% = 0.01

= P ( Z < $(\frac{3.95 - u }{0.02})$ ) = P ( Z < -2.3263 ) = 0.01

therefore :

$(\frac{3.95 - u }{0.02})$  = -2.3263

hence : u = 3.996 inches ( mean diameter )

B) At mean diameter = 3.98 calculate the value of std

P ( X < 3.95 ) = 0.01

= P ( Z < $( \frac{3.95-3.98 }{std } )$ )  = P ( Z < -2.3263 ) = 0.01

therefore

$( \frac{3.95-3.98 }{std } )$ = -2.3263

hence std = 0.01 inch

C) option B is preferable because its mean diameter is smaller and  the percent of lids too large to fit is considered more carefully using option B