3. A soft-drink machine is regulated so that it discharges an average of 200 mil

Question

3. A soft-drink machine is regulated so that it discharges an average of 200 milliliters per cup. If the amount of drink is normally distributed with a standard deviation equal to 15 milliliters, a. What fraction of cups will probably overflow if 230-milliliter cups are used for the next 1000 drinks? b. What is the probability that a cup contains between 191 and 209 milliliters? c. Above what value do we get the largest 10% of the drinks? d. Suppose a sample of size 16 is taken. What is the probability that the sample mean is greater than 208 milliliters? e. Does your answer to part (d) provide evidence to dispute the claim that the average fill is 200 milliliters per cup? Explain your answer.

Explanation / Answer

Here it is given mean=200 and sd=15

a. P(x>230)=P(z>230-200/15)=P(z>2)=0.0228

b. P(191<x<209)=P(-0.6<z<0.6)=0.4515

c. P(Z>z)=0.10

z=1.282=x-200/15=219.23

d. P((xbar>208)=P(z>(208-200/(15/4))=P(z>2.13)=0.0166

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