If you are using Excel to do these calculations for any of the problem, please i

Question

If you are using Excel to do these calculations for any of the problem, please include these with the answer to problem 5 and 10. This is for partial credit if something is not correct. 1. (Normal Distribution) "Extra Excellent Foods America" only wants to sell the best oranges. They have that determined the best oranges have diameter of 2.375". The will only buy oranges have diameters of 2.375"+/- 0.125". Their vendor supplies oranges that have an average diameter of 2.500" with a standard deviation of 0.175". The vendor offers 1000 oranges per batch. How many oranges per batch, on average, will be accepted?

Explanation / Answer

here tolerance limit are 2.375-0.125 to 2.375+0.125 or 2.25 to 2.50

here as we know from normal disribution that z=(X-mean)/std deviation

hence P(2.25<X<2.5)=P((2.25-2.5)/0.175<z<(2.5-2.5)/0.175)=P(-1.4286<Z<0)=0.5-0.0766=0.4234

hence accepted oranges out of 1000 =np=1000*0.4234=423.4~423

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