Austin asked Jeremy how far from the building the base of the ladder was. Jeremy did the problem and showed his work below. Aust
in thinks you should find c, the hypotenuse whereas Jeremy thinks you should find b. Find the distance between the ladder and house. Round to the nearest tenth if possible.
1 answer:
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Nice job with part A on getting those correct answers.
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Part B
- mu = mean = 43
- sigma = standard deviation = 3
Let's calculate the z score for the raw score x = 37
z = (x - mu)/sigma
z = (37 - 43)/3
z = -6/3
z = -2
A negative z score tells us we're below the mean. Specifically, we are exactly 2 standard deviations under the mean.
If you repeat those steps for x = 46 (not changing mu or sigma), then you should get z = 1. So we're now 1 standard deviation above the mean.
Ultimately, we want to know the area under the standard normal curve (aka z curve) from z = -2 to z = 1.
Refer to the chart below which is a breakdown of the Empirical Rule. The pink areas are within 1 standard deviation of the mean. We have two regions taking up roughly 34% of the full area under the curve, so they combine to 34+34 = 68%
Then we add on another 13.5% which is the blue area on the left (between z = -2 and z = -1)
So 13.5+68 = 81.5% of the area under the curve is between z = -2 and z = 1.
<h3>Answer: 81.5</h3>Note: the percent sign is already taken care of for us, so there's no need to type it in. But the answer above of course means 81.5% and that answer is approximate.
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Part C
Let's find the z score for x = 34. The values of mu and sigma are the same as before.
z = (x - mu)/sigma
z = (34-43)/3
z = -9/3
z = -3
So computing P(X > 34) is the same as P(Z > -3)
Notice how adding up all of the values in the chart mentioned gets us:
2.35+13.5+34+34+13.5+2.35 = 99.7
which means 99.7% of the distribution is within 3 standard deviations of the mean. The remaining 100% - 99.7% = 0.3% is the combined area of both tails. So each tail is (0.3%)/2 = 0.15%
In short, 0.15% of the area under the curve is to the left of z = -3
Therefore, 100% - 0.15% = 99.85% of the widgets are going to have z values larger than -3, which in turn means they have values larger than 34.
<h3>Answer: 99.85</h3>Again you don't have to worry about the percent sign. Like before, the answer is approximate.
