Which percentage is the best estimate for the shaded area under this normal curve?

Explanation:

It appears that -20 is the mean. It's not entirely clear however. If that assumption is correct, then the distance from -30 to -20 is 10 units. So the left endpoint is 1 standard deviation below the mean (because the standard deviation is 10 units).

Recall that through the empirical rule, roughly 68% of the distribution is within 1 standard deviation of the mean. This cuts in half to 34%. So the area from x = -30 to x = -20 is roughly 0.34

We'll use this value later so let A = 0.34

The area under the curve from x = -20 to x = -10 is also 0.34

The area under the curve from x = -20 to x = 0 is 0.95/2 = 0.475

For the second part there, I'm using the idea that 95% of the normal distribution (roughly) is within 2 standard deviations of the mean.

So the area from x = -20 to x = -5 is somewhere between 0.34 and 0.475

Let B = 0.34 and C = 0.475

The full shaded blue area is somewhere between A+B = 0.34+0.34 = 0.68 and A+C = 0.34+0.475 = 0.815

Based on that alone, the answer is between B and C.

Unfortunately, we can't nail down an actual value unless we use a Z table or a calculator.

When I use a calculator, I'm getting 0.7745 (approximate) which rounds to 0.775 and converts to 77.5%

As for how to get this without a table or calculator, I'm not entirely sure what your teacher wanted you to do.

well.. let me think..

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Martha was eating pizza. 6/15 of that pizza had already been eaten. what could you multiply 6/15 by to get 15?

I really don't know rn. By brain is still LOADING