The manager of a local soft-drink bottling company believes that when a new beve
ID: 3174923 • Letter: T
Question
The manager of a local soft-drink bottling company believes that when a new beverage dispensing machine is set to dispense 7 ounces in each of its bottles, but it in fact dispenses varying amounts. The amount of soda dispensed per bottle has a mean of 7.00 ounces and a standard distribution of 0.23 ounces. Suppose the manager randomly selects one hundred bottles that were filled by this company’s filling machine. What is the probability that the mean amount of this manager’s sample is less than 6.9 ounces?
Explanation / Answer
here std error =std deviation/(n)1/2 =0.023
from normal distribution z=(X-mean)/std error
henc eP(X<6.9)=P(Z<(6.9-7)/0.023 =P(Z<-4.3478)=0.00000687
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