Mean diameter of holes produced by a drilling machine bit is 4.05 mm and the standard deviation of the diameters is 0.0028 mm. For twenty holes drilled using this machine, determine, correct to the nearest whole number, how many are likely to have diameters of between:

(a) 4.048 and 4.0553 mm,

and

(b) 4.052 and 4.056 mm

*assuming the diameters are normally distributed.

Explain the concept and calculation of the confidence interval.