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When a triangle is rotated, it must be rotated through a center of rotation.
Assume the coordinate of LMN is
The rule of 180-degree rotation is:
So, we have:
See attachment for the graphs of LMN and L'M'N
<u>(a) Describe the transformation</u>
When triangle LMN is rotated 180 degrees across the origin, the x and y coordinates of LMN are negated to form triangle L'M'N'
<u>(b) Lines LL' and MM'</u>
The distance between point L and the center of origin is the same as the distance between point M' and the center of origin
Similarly, the distance between point L and the center of origin is the same as the distance between point M' and the center of origin
<u>(c) Line NN'</u>
Line NN' will assume the same characteristics as lines LL' and MM'
Read more about transformations at:
Answer:
(a) The sampling distribution of = Population mean = 79
(b) P ( greater than 81.2 ) = 0.1357
(c) P ( less than or equals 74.4 ) = .0107
(d) P (77.6 less than less than 83.2 ) = .7401
Step-by-step explanation:
Given -
Sample size ( n ) = 81
Population mean = 79
Standard deviation = 18
(a) Describe the sampling distribution of
For large sample using central limit theorem
the sampling distribution of = Population mean = 79
(b) What is Upper P ( greater than 81.2 ) =
=
=
=
= 1 - .8643 =
= 0.1357
(c) What is Upper P ( less than or equals 74.4 ) =
=
=
= .0107
(d) What is Upper P (77.6 less than less than 83.2 ) =
=
=
=
= 0.9821 - .2420
= 0.7401