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il63 [147K]
3 years ago
15

The water level In a plastic pool changed by the -8 gallons each hour due to a small hole in the bottom after 6 hours the pool c

ontained 132 gallons how much water was in the pool originally
Mathematics
1 answer:
vlada-n [284]3 years ago
5 0

Answer:

180 gallons

Step-by-step explanation:

Each hour, 8 gallons were lost. Thus, in 6 hours,

6 * 8 = 48 gallons were lost

After 6 hours, 132 gallons remained, so before this 6 hours, there were more 48 gallons in it. Thus,

Original amount was 132 + 48 = 180 gallons

Originally, 180 gallons of water was in the pool

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How do you solve the question solve for n 1/3 n = 6
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5
masya89 [10]

Answer:

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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 grade points avergae of a population, and for this case we know the following properties

Where \mu=2.54 and \sigma=0.45

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

z= \frac{3.44-2.54}{0.45}=2

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

P(X>3.44) = P(Z>2) = 0.025

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3 years ago
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