I am practising normal distribution exam type questions but I am stuck at this one:
The masses of individual apples sold in a food store are normally distributed. The supplier who provides the store with apples knows that 75% of the apples have a mass greater than 85 grams and that 10% of the apples have a mass greater than 120 grams.
(a) Find the value of the mean and the value of the standard deviation
So I successfully found the mean (
μ=97.1) and the standard deviation (
δ=17.9) by calculating the z-scores of the given probabilities.
The apples are always sold in bags containing 6 apples.
So how do I find the following probabilities for the grouped items? Do I have to use binomial distribution (6 trials) or something else?
(b) Find the probability that each apple in a randomly selected bag has a mass less than 105 grams.
(c) How many apples (to the nearest whole number) from a randomly selected bag would you expect to have a mass greater than 90 grams?
Thank you for the guidance in advance!