Can you answer the following question for part a, b, c, & d showing the formula used and working out.

Diameters of bolts produced by a particular machine are normally distributed with mean 0.760cm

and standard deviation 0.012cm. Specifications call for the diameters to range from 0.730cm to

0.780cm

a) What proportion of bolts will be smaller than 0.740cm?

b) What value of the diameter is exceeded by 10% of the bolts?

c) What proportion of bolts will meet the specification?

d) What value of the standard deviation is required so that less than 3% of the bolts have a diameter

greater than 0.78cm?