Proportion of contents

Question

A company supply one of major products in 1 liter canisters. Company past records shows that the amount of caustic materials in one liter of the product averages 48 grams with a standard deviation of 7 grams.

What proportion of the 1 liter canisters will have more than 50g of caustic material?

What proportion of the 1 liter canisters will have between 42g and 52g of caustic material?

Answer 1

In order to find the proportion of the 1 liter canisters will have more than 50g of caustic material, we need to find how many standard deviations or the Z score that 50 is by the calculation

 

Z of 50= (50-48)÷7 = .2857; and since we want greater than 50 grams, we are looking for the area under the curve of the normal distribution that is greater than .2857 Z. Looking at a Z table (or using Excel), we find that 0.387548481 or 38.76% of the canisters will have greater than 50 grams

 

Likewise for the second problem, we calculate the probability of being less than 52 grams and the probability of being less than 42 grams and subtract the two. The Z score of 52 grams is (52-48)÷7 =.5714 which gives us a probability of 0.716145417 or 71.6145% will be below 52. Similarly, the score of 42 grams is (42-48)÷7 =.-.8571 which gives us a probability of 0.195682969 or 19.568% will be below 42. The difference is 71.6145% less  19.568% or 0.520462448 or 52.046% of the canisters will have between 42 and 52 grams.

 

Biggest hint is to always turn the raw numbers into Z scores that you can look up in a Z table or use the norm.s.dist function in Excel.

 

Hope this helps,

 

Walter