Question 1
Paper 1Hard8 marksAt a cereal plant, the mass in grams, of a randomly selected bag is modelled by a normal distribution with mean g and standard deviation g. A bag is accepted if its mass is at least g.
The machine can be adjusted by adding the same amount grams to the mass of every bag. This adjustment does not change the standard deviation.
Write down the interval that contains approximately of the bag masses at the current setting.
Use your GDC to find the probability that a randomly selected bag is accepted at the current setting. Give your answer to four significant figures.
The manager requires at least of the bags to be accepted. Using your answer to (b), state whether the current setting meets this requirement. Determine the smallest value of that meets the requirement. Give your answer to three significant figures.