The amount of potassium in food varies, but bananas are often associated with high potassium, with approximately 422 mg in a medium-sized banana.† Suppose the distribution of potassium in a banana is normally distributed, with mean equal to 422 mg and standard deviation equal to 18 mg per banana. You eat n = 7 bananas per day, and T is the total number of milligrams of potassium you receive from them. (a) Find the mean and standard deviation of T (in mg). (Round your standard deviation to four decimal places.) mean mg standard deviation mg (b) Find the probability that your total daily intake of potassium from the seven bananas will exceed 3,000 mg. (Round your answer to four decimal places.)

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step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

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