What is the surface area of the figure shown above?
2 answers:
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Answer:
0.7698
Step-by-step explanation:
If you call your random variable , then what you are looking for is
because you want the probability of being <em>between 87 and 123.</em>
We need a table with of the normal distribution. But we can only find the table with and
. Because of that, first we need to <em>normalize </em>our random variable:
(you can always normalize your variable following the same formula!)
now we can do something similar to our limits, to get a better expression:
And we transform our problem to a simpler one:
(see Figure 1)
From our table we can see that (this is represented in figure 2).
Remember that the whole area below the curve is exactly 1. So we can conclude that (because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then
.
FINALLY:
