Question

Suppose your favorite coffee machine offers 14 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal​ distribution, with mean equal to 15 ounces and standard deviation equal to 0.7 ounces. For each part sketch a​ graph, mark the​ mean, and shade the area to which the answer refers and compute the percentage. Complete parts a through c.

a. What percentage of cups will be filled with less than 14 ​ounces?

b. what percentage of cup that will be filled with more than 14.5 ounces is %?(graph)

c. what percentage of cups will have between 14 and 15 ounces of coffee? (percent and graph)

Answer 1

a)

probability =P(X<14)=(Z<(14-15)/0.7)=P(Z<(-1.4286)=0.0766~ 7.66 %

b)

probability =P(X>14.5)=P(Z>(14.5-15)/0.7)=P(Z>-0.71)=1-P(Z<-0.71)=1-0.23753=0.7625~ 76.25%

c)

probability =P(14<X<15)=P((14-15)/0.7)<Z<(15-15)/0.7)=P(-1.43<Z<0)=0.5-0.0766=0.4234~ 42.34%