A technical installation produces nails with an average length of 10 cm. The length of the nails produced is normally distributed with a standard deviation of 2 mm. (PLEASE SHOW FORMULA AND PROCEDURE)
a) What is the median of this normal distribution?
b) What is the probability that a randomly selected nail is shorter than 10.4 cm?
c) What percentage of the nails are between 9.9 and 10.1 cm long?
d) What is the minimum length of 80% of the nails. That is, what length is exceeded by 80% of all nails?
e) The random variables X and Y with E(X) = 10, E(Y) = 7, σ(X) = 4 and σ(Y) = 3 are normally distributed. Under suitable conditions determine - name them - the distribution of the random variable Z = X + Y.
f) Why can the length of nails only be approximately normally distributed?