SAT scores of students at an Ivy League college are distributed with a standard deviation of 250 points. Two statistics students
, Raina and Luke, want to estimate the average SAT score of students at this college as part of a class project. They want their margin of error to be no more than 25 points.(a) Raina wants to use a 90% condence interval. How large a sample should she collect?Raina should sample at least people.
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Answer:
and as
Step-by-step explanation:
Given
-- Missing from the question
Required
The behavior of the function around its vertical asymptote at
Expand the numerator
Factorize
Factor out x + 1
We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)
We are only interested in the sign of the result
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As x approaches -2 implies that:
Say x = -3
We have a negative value (-12); This will be called negative infinity
This implies that as x approaches -2, p(x) approaches negative infinity
Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)
As x leaves -2 implies that:
Say x = -2.1
We have a negative value (-56.1); This will be called negative infinity
This implies that as x leaves -2, p(x) approaches negative infinity
So, the behavior is:
and as