A cracker manufacturer’s boxes have been found to have a standard deviation of 10 grams and a mean of 412 grams.

How many grams should be specified (printed on the box) to ensure that 95 percent of the boxes will contain more than this weight?

395.55 grams should be specified to ensure that 95 percent of the boxes will contain more than this weight.

Explanation:

We are given the following information in the question:

Mean, μ = 412 grams

Standard Deviation, σ = 10 grams

Formula:

We have to find the value of x such that the probability is 0.95

P(X > x)  

Calculation the value from standard normal z table, we have,  

Hence, 395.55 grams should be specified to ensure that 95 percent of the boxes will contain more than this weight.

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