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The amount of soft drink that Ann consumes on any given day is independent of consumption onany other day and is normally distributed with $\mu=13$ oz and $\sigma=2 .$ If she currently has twosix-packs of 16 -oz bottles, what is the probability that still has some soft drink left at the endof 2 weeks $(14$ days) . Why should we worry about the validity of the independence assumptionhere?

.9099

Intro Stats / AP Statistics

Chapter 4

Joint Probability Distributions and Their Applications

Section 11

Supplementary Exercises

Probability Topics

The Normal Distribution

Sani E.

October 28, 2020

The amount of soft drink that Ann consumes on any given day is independent of consumption on any other day and is normally distributed with µ = 13 oz and ? = 2. If she currently has two six-packs of 16-oz bottles, what is the probability that she has some

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So we're given that This person and consumes a mean value of 13 oz of soft drink a day, with a standard deviation of two ounces, and it's distributed normally. And what we're trying to find is Given that she has 26 packs of 16 ounce bottles of soft drink, what the probability is that she will have some Amount of soft drink left over after 14 days. And so the first thing we want to do is get the amount of soft drinks she has in ounces, and so she has a six pack, she has two of those, And they're all at 16oz. So it is six times two times 16, Which comes out to be 192. And so this is the amount of ounces of soft drinks she actually has. So we want to find the probability that The amount of soft drink that she is actually consumed is less than 192, she should be less than And so how we're gonna do this is we're going to use a Z score where we let Z equal our x minus you over. Yeah, the standard deviation multiplied by our number of trials are in the state, number of days, in this case, number of days, And then we're going to transform our normal distribution into a standard normal distribution so that we can look at the standard table for our values. So for this hour you is just our mean value, which is 13, So use 13. And then we multiply the amount of days That we are doing this since our 13 is the mean value over one day and we want to find the main value over 14 days. So we multiply by 14 and this comes out to be 182. So what we do now is we can say that RPFX is less than 192, is equal to P of Z is less than one 92 -182, divided by our standard deviation, which is two, multiplied by The amount of days square rooted, which is 14. And now we just need to find what this number is, and then look at the standard normal table for our value, so this is equal to P of Z is less than 10/2 Squares 14. And if you plug this into calculator, You'll see that 10-2 squares of 14 is Equal to about 1.34. And so now, if we go look at our normal distribution table, we'll see that the probability that C is less than 1.34 is about .9099.

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