Your manufacturing company sells metal nuts and bolts that come together in a package. The diameter of the bolts coming off the factory line follows a normal distribution with mean 20mm and standard deviation 0.12mm. The diameters of the holes in the nuts follow a normal distribution with mean 20.7mm and standard deviation of 0.09mm. Assume that in order for a nut and bolt to fit together the diameter of the hole in the nut has to be between .5 and .9 mm larger than the bolt.

a. Find the Z-score for a
Bolt of 20.168mm:
Nut of 20.547mm:

b. How many standard deviations away from the average is a bolt with a diameter of 20.036mm?
c. Which is more likely
i. Bolt larger than 20.168mm
ii. Bolt smaller than 19.784mm

d. Which is more likely
i. Bolt larger than 20.3mm
ii. Nut smaller than 20.502mm

e. About 50% of nuts are smaller thanmm
f. About 95% of bolts are approximately betweenmm and mm
g. About 99.7% of nuts are approximately between mm and mm