A chemist can set the target value for the elasticity of a polymer compound. The resulting elasticity is normally distributed with a mean equal to the target value and a standard deviation of 47.
(a) What target value should be set if it is required that there is only a 10% probability that the elasticity is less than 800?
(b) Suppose that a target value of 850 is used. What is the probability that the average elasticity of 10 samples is smaller than 875?