Cans of regular Pepsi are labeled as containing twelve ounces. Assume that the a

Question

Cans of regular Pepsi are labeled as containing twelve ounces. Assume that the actual contents of all cans are normally distributed with a mean of 12. 29 ounces and a population standard deviation of 0.09 ounces. Determine the probability that an individual can of Pepsi, randomly selected, has less than twelve ounces? Interpret these probability more than twelve ounces? Interpret this probability. Explain the importance to the consumer of your answer in # 1 and in # 2. Determine the following percentiles for individual cans of regular Pepsi: the 95^th percentile the 5^th percentile Determine the interval of ounces for the middle 90% for individual cans of regular Pepsi. Pepsi is very concerned with marketing their product to the consumer. Explain, using your answers from # 1 through # 5, the benefits to the consumer. (Minimum of five sentences...)

Explanation / Answer

Here it is given mean=12.29 and sd=0.09

1. Here we need to find P(x<12)

As it is given its normal we will convert this to z

P(x-mu/sd<12-12.29/0.09)=P(z<-3.22)=0.5-P(-3.22<=z<=-0)=0.5-0.4994=0.0006, which means very less can will have volume less than 12 ounces

2. Here we need to find P(x>12)

As in a we will convert x to z as P(z>12-12.29/0.09)=P(z>-3.22)=0.5+0.4994=0.9994

It means many cans are having volume greater than 12

3. A and b can help us to check whether our cans are being filled over or under and corrective actions can be taken.

4. z value for 95% percentile is 1.645

So P(z<1.645)=0.95

Now converting z to x

As we know z=x-mu/So x=1.645*0.09+12.29=12.44

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