A publisher has discovered that the number of words contained

A publisher has discovered that the number of words contained in a new manuscript is normally distributed with a mean equal to 20,000 words in excess of that specified in the authors’s contract and a standard deviation of 10,000 words.  If the publisher wants to be almost certain (say with a probability of .95) that the manuscript will be less than 100,000 words, what number of words should the publisher specify in the contract?

 

Please explain the process to do so, as well as the correct answers.

 

My answers were as follows:

a) 0.0239

b) 0.9693

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