A certain synthesis technique performed by a company every day for the past 10 y

Question

A certain synthesis technique performed by a company every day for the past 10 years gives a yield that follows a Gaussian distribution, with a mean of 58.205 g and a standard deviation of 3.680. (You can use the data found here - https://sites.google.com/site/chempendix/statistiics/ordinate-and-area-for-a-normal-error-curve - or the data found in your text to help you with this question.)

What is the fraction of syntheses that will give a yield of over 62.253 g?  

What is the fraction of syntheses that will give a yield of between 50.845 and 52.317 g?  

Explanation / Answer

mean is 58.205 and standard deviation is 3.68

a) P(x>62.253)=P(z>(62.253-58.205)/3.68)=P(z>1.1)=1-P(z<1.1), from normal distribution we get =1-0.8643=0.1357

b) P(50.845<x<52.317)=P((50.845-58.205)/3.68<z<(52.317-58.205)/3.68)=P(-2<z<-1.6) =P(1.6<z<2)=P(z<2)-P(z<1.6) , from normal distribution table we get 0.9772-0.9452=0.032

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