Paula is painting a henhouse. If a can of paint will cover 24 square feet, how many cans of paint does she need to buy? Explain
1 answer:
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Answer:
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".
Solutio to the problem
Let X the random variable that represent the amount of beer in each can of a population, and for this case we know the distribution for X is given by:
Where and
For this case we select 6 cans and we are interested in the probability that the total would be less or equal than 72 ounces. So we need to find a distribution for the total.
The definition of sample mean is given by:
If we solve for the total T we got:
For this case then the expected value and variance are given by:
And the deviation is just:
So then the distribution for the total would be also normal and given by:
And we want this probability:
And we can use the z score formula given by:
Answer:
5.83
Step-by-step explanation:
Find the mean:
10(.1) + 15(.2) + 20(.2) + 25(.4) + 3-).1)
u = 21
Find the standard deviation:
= 5.83