Question

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.Bags in the top 5% contains too much oats and must be repackaged. That is the smallest weight a bag could have and still needs to be repackaged?

Answer 1

Solution:-

Given that,

mean = = 1000

standard deviation = = 150

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95  

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 150 + 1000

x = 1246.75 grams.