20 points please help me i need this answer
1 answer:
The statements that are TRUE regarding the box plots are:
A, D, and E.
The box plots are given in the image attached below.
<h3>The Five-number Summary Displayed by a Box Plot</h3>The values displayed by a box plot for a given data are:
- Median
- Minimum
- Maximum
- First Quartile
- Third Quartile
Interquartile range = Third Quartile - First Quartile.
Thus, shelter's A median is 21, shelter B's 18.
Interquartile range for shelter A = 28 - 8 = 20
Interquartile range for shelter B = 28 - 10 = 18
<h3>What is a Symmetric Data Set?</h3>- If a data set is symmetric, a box plot that represents the data set will have the median in the middle of the box, while both whiskers will be about the same on both sides of the box.
- For example, the data set for shelter B is symmetric.
Therefore, the statements that are TRUE regarding the box plots are:
A, D, and E.
Learn more about box plots on:
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DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!
<h2>(a)</h2>Case 1: both balls are white.
At the beginning we have balls. We want to pick a white one, so we have a probability of
of picking a white one.
If this happens, we're left with white balls and still
black balls, for a total of
balls. So, now, the probability of picking a white ball is
The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability
Case 2: both balls are black
The exact same logic leads to a probability of
These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is
Case 1: both balls are white.
In this case, nothing changes between the two picks. So, you have a probability of of picking a white ball with the first pick, and the same probability of picking a white ball with the second pick. Similarly, you have a probability
of picking a black ball with both picks.
This leads to an overall probability of
Of picking two balls of the same colour.
<h2>(c)</h2>We want to prove that
Expading all squares and products, this translates to
As you can see, this inequality comes in the form
With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:
And this is our case, because in our case we have
so, y has an extra piece and it is larger
which ensures that k<x (and thus k<y), because b and w are integers, and so b<b^2 and w<w^2