Suppose your favorite coffee machine offers 9 ounce cup of coffee. The actual am

Question

Suppose your favorite coffee machine offers 9 ounce cup of coffee. The actual amount of coffee put in the cup machine varies according to a normal distribution, with equal to 10 ounces and standard deviation equal to .74 ounces. For each part sketch a graph, mark the mean and shade the area to which the answer refers and compute the percentage. What percentage of cups will be filled with less than 9 ounces? (B) What percentage of cups will be filled with more than 9.7 ounces? (C) what percentage of cups will have between 9 and 10 ounces of coffee?

Explanation / Answer

from normal distribution zscore =(X-mean)/std deviation

a) P(X<9)=P(Z<(9-10)/0.74)=P(Z<-1.3514)=0.0883~8.83%

b)P(X>9.7)=1-P(X<9.7)=1-P(Z<-0.4054)=1-0.3426=0.6574~65.74%

c)P(9<X<10)=P(-1.3514<Z<0)=0.5-0.0883=0.4117~41.17%

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