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jonathanspears1
19.03.2020 •
Mathematics
The number of gallons of carbonated soft drink consumed per person annually is normally distributed with mean 47.5 and standard deviation 3.5.The probability that a randomly selected person consumes between 45 and 50 gallons of carbonated soft drink per year is about:
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Ответ:
And we can find this probability with the following difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the number of gallons of a population, and for this case we know the distribution for X is given by:
Where
and ![\sigma=3.5](/tpl/images/0554/4744/fa4b4.png)
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the following difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Ответ: