SOLUTION: A food shop buys organic oats in bags of mean weight 1000 grams. It is known that the weights of the bags in any batch are normally distributed with standard deviation 150 grams. A

Question 1131547: A food shop buys organic oats in bags of mean weight 1000 grams. It is known that the weights of the bags in any batch are normally distributed with standard deviation 150 grams. A bag of oats is randomly selected, calculate the following probabilities, rounding your final answers to 4 decimal places.
a) The bag is exactly 750 grams
(b) The bag is less than 1225 grams
(c) The bag is more than 700 grams
(d) The bag is either less than 700 grams or more than 1225 grams
(e) The bag is between 700 and 1225 grams
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a.probability 0 for a continuous distribution, since each point is dimensionless.
b. This is z< (x-mean)/sd which is z< 225/150 or z<1.5
This has probability 0.9332
c. This has a z>-300/150 or z> -2 or probability of 0.9772
d. This has z<-2 or z>+1.5 with probability 0.0228+0.0668 or 0.0896
e. This is the complement of d or 0.9104 probability

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