Help Me With This #Geometry
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<h3>The exact probability that the blue ball is drawn first and the red ball is drawn second is 
</h3>
<em><u>Solution:</u></em>
<em><u>The probability of an event is given as:</u></em>
Given that,
There are 12 balls in a bag
One is blue and one is red
Favorable outcome = blue ball is drawn first
Favorable outcome = 1
Therefore,
Now, without replacement, red ball is drawn second
Therefore,
Total possible outcomes = 12 - 1 = 11
<em><u>What is the exact probability that the blue ball is drawn first and the red ball is drawn second?</u></em>
Thus the exact probability that the blue ball is drawn first and the red ball is drawn second is
Answer:
And if we solve for a we got
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 hourly rates of a population, and for this case we know the distribution for X is given by:
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got