A company that manufactures and bottles apple juice uses a

Chapter 4, Problem 63E

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QUESTION:

A company that manufactures and bottles apple juice uses a machine that automatically fills 16-ounce bottles. There is some variation, however, in the amounts of liquid dispensed into the bottles that are filled. The amount dispensed has been observed to be approximately normally distributed with mean 16 ounces and standard deviation 1 ounce.

a Use Table 4, Appendix 3, to determine the proportion of bottles that will have more than 17 ounces dispensed into them.

b Applet Exercise Use the applet Normal Probabilities to obtain the answer to part (a).

Questions & Answers

QUESTION:

A company that manufactures and bottles apple juice uses a machine that automatically fills 16-ounce bottles. There is some variation, however, in the amounts of liquid dispensed into the bottles that are filled. The amount dispensed has been observed to be approximately normally distributed with mean 16 ounces and standard deviation 1 ounce.

a Use Table 4, Appendix 3, to determine the proportion of bottles that will have more than 17 ounces dispensed into them.

b Applet Exercise Use the applet Normal Probabilities to obtain the answer to part (a).

ANSWER:

Solution :

Step 1 of 2:

Let Y be a bottle apple juice uses a machine that automatically fills 16-ounce bottles.

We know that Y follows a normal distribution with mean and standard deviation .

Here mean =16 ounces and standard deviation =1 ounce.

Our goal is:

a). We need to find the proportion of the bottles that will have more than 17 ounces dispensed

      into them.

b). If we use the applet normal probabilities to obtain the answer to part (a).

Now we have to find the proportion of the bottles that will have more than 17 ounces dispensed into them.

The probability of Y will have more than 17 ounces is

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