The figure shows a triangle with its three angle bisectors intersecting at Point P.
1 answer:
Check the picture below.
we know the lines are angle bisectors, so the line makes twin angles, so the line FP is making twin angles, we also know the angle FZP and the angle FYP are right-angles, as well as FP is a common hypotenuse to two right triangles, thus by the HA postulate for right triangles, triangle FPZ and triangle FPY are both congruent, so their sides are also congruents, thus PY = PZ.
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Part a)
The simple random sample of size n=36 is obtained from a population with
and
The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.
Therefore the sampling distribution has a mean of
The standard error of the means becomes the standard deviation of the sampling distribution.
Part b) We want to find
We need to convert to z-score.
Part c)
We want to find
We convert to z-score and use the normal distribution table to find the corresponding area.
Part d)
We want to find :
We convert to z-scores and again use the standard normal distribution table.