Finding mean and standard deviation: Example

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced, weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. What are the mean and standard deviation?

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Given P( )=22.57%=0.2257

Look for tables of standard normal distribution tables and find the value of Z corresponding to area=0.2227, we get Z=0.60

We will consider ...