Statistic Method question , please help to me about it

Question

4. In a certain company, the weekly use of a raw material, is a v.a. with normal distribution parameters p = 600 Kg e c = 40 Kg. Earlier in a certain week the company has in stock 634Kg of raw material, being impossible this week receive more supplies.

 

4.1. Determine the probability of unavailability of the raw material that week.

 

4.2. What is the probability of a given week the consumption is below average, given that earlier this week already consumed at least 500 kg of raw material?

 

 

Answer 1

We expect to use 600kg of materials, with a standard deviation of 40kg. We have 634kg. Doing this by hand/with a Normal table, first find the Z score for 634: Z = (x-mu)/sigma in general. In our case, that means Z = (634 - 600)/40 = 0.85 If we look up this Z score in the Normal distribution table, we find there's a 0.8023 chance of getting a Z score this low or lower.

Question 4.1 asks what's the probability we use MORE than 634kg of material. The answer to that question is 1-.8023 = .1977. This is the answer you'll get if you just do normalcdf(634, 10000,600,40) on your TI calculator or 1- NORM.DIST(634, 600, 40,1) in Excel.

Question 4.2 is a conditional probability. In general, the formula for P(A | B), "The probability of A given B", is P(A^B)/P(B), "The probability of A and B being true, divided by just the probability of B being true". In our case, The probability of being 500 or greater is .9938. The probability of being above 634 is .1977, so the probability of being above 634 given that we're already above 500 is 0.1977/0.9938 = 0.1989