A company makes oven doors for use in the manufacture of electric cookers. The width of the doors has a mean of 850 mm. When production is satisfactory, the width of the doors is known to be normally distributed with standard deviation 0.8 mm. A door is randomly selected, calculate the following probabilities, rounding your final answers to 4 decimal places.

(a) The door is between 848.4 mm and 851.2 mm

(b) The door is less than 848.4 mm

(c) The door is more than 851.2 mm

(d) The door is either less than 848.4 mm or more than 851.2 mm

(e) The door is exactly 850 mm.

(f) Doors in the bottom 5% will not meet industry standards and must not be packaged for sale. What is the largest door that would not meet industry standards?