A process manufacturers ball bearings whose diameters are normally distributed w

Question

A process manufacturers ball bearings whose diameters are normally distributed with a mean diameter of 2.50 cm, the center of the specification interval. Specifications call for the diameter to be in the interval 2.50 0.01 cm. The standard deviation of the process is 0.008 cm. What proportion of the diameters will meet the specifications? Round to nearest hundredth.

To what value must the standard deviation in the previous problem be lowered so that 95% of the diameters will meet the specification?

Explanation / Answer

specificaions are 2.51 and 2.49

the process have mean 2.50 and SD of 0.008

P( 2.49 < x < 2.51 ) ???

P( 2.49 - 2.50 / 0.008 < z < 2.51 - 2.50 / 0.008 )

P( -1.25 < z < 1.25 ) = 1 - 0.1056 - 0.1056 = 0.7888

78.88% will meet the specifications

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.