On a field trip there were 5 girls for every 8 boys. How many girls attended the 130 student trip?
2 answers:
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Answer:
<em>Pool 1 leaks faster than pool 2.</em>
Step-by-step explanation:
<u>Rates of change</u>
The rate of change (ROC) is a measure that compares two quantities, usually to know how fast one variable changes in time.
We are given two rates of change for two pools that are leaking. The first one loses 2/3 gallon in 15 minutes, and the other loses 3/4 gallon in 20 minutes.
To compare them, we are required to express time in hours. Recall one hour has 60 minutes, or equivalently, one minute has 1/60 hours. Converting both times, we have:
15 minutes = 15/60 = 1/4 hours
20 minutes = 20/60 = 1/3 hours
Now compute both rates of change:
Pool 1:
Pool 2:
Comparing both ratios, it's clear pool 1 leaks faster than pool 2.
Answer:
And we can ue the z score formula given by:
And using this formula we got for the limits:
So we want to find this probability:
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 annual income of a population, and for this case we know the following info:
and
and we are omitting the zeros from the thousand to simplify calculations
We select a sample size of n=50>30.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean is given by:
And we want to find this probability:
And we can ue the z score formula given by:
And using this formula we got for the limits:
So we want to find this probability: