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We have been given graph of a downward opening parabola with vertex at point . We are asked to write equation of the parabola in standard form.
We know that equation of parabola in standard form is .
We will write our equation in vertex form and then convert it into standard form.
Vertex for of parabola is , where point (h,k) represents vertex of parabola and a represents leading coefficient.
Since our parabola is downward opening so leading coefficient will be negative.
Upon substituting coordinates of vertex and point (0,0) in vertex form, we will get:
Divide both sides by
So our equation in vertex form would be .
Let us convert it in standard from.
Therefore, the equation of function is standard form would be .
You're looking for a value 
such that
Because the distribution is symmetric, the value of in either case will be the same.
Now, because the distribution is continuous, you have that
The mean for the standard normal distribution is
, and because the distribution is symmetric about its mean, it follows that 
.
You can consult a score table to find the corresponding score for this probability. It turns out to be 
.
Because the distribution is symmetric, the value of
Now, because the distribution is continuous, you have that
The mean for the standard normal distribution is
You can consult a