I think there's an easy way and a hard way to do this, and I think that the way
I'm about to describe is the easier way.
Probability = (number of successful outcomes)/(total number of possible outcomes)
<em>How many total pairs can be drawn from 8 total pens ?</em>
-- The first one drawn can be any one of 8 pens. For each of these . . .
-- The second one drawn can be any one of the remaining 7 .
-- Total number of ways of drawing a pair = (8 x 7) = 56 ways.
-- But there aren't 56 different different pairs. Whether you draw A and then B,
or B and then A, you wind up with the same pair. There are 2 different ways to
draw each pair, so the 56 ways of drawing a pair only produces <u>28</u> different pairs.
<u>How many pairs are two of the same color ?</u>
<em>Possible number of blue pairs:</em>
The reasoning is exactly the same as calculating the TOTAL number of
pairs, as explained above.
With 5 blue pens, you can make <u>10</u> different pairs.
AB, AC, AD, AE, BC, BD, BE, CD, CE, and DE.
<em>Possible number of red pairs:</em>
The reasoning is exactly the same as calculating the TOTAL number of
pairs, as explained above.
With 3 red pens, you can make <u>3</u> different pairs.
AB, AC, and BC.
Total number of possible same-color pairs = 10 + 3 = 13
successes / total possible outcomes = 13/28 = <u>46.4</u>% (rounded)
The measure of angle B is 97°
Sample size= n= 84
sample mean= x = 107 s
population standard deviation =σ= 11.7
As, population standard deviation is given so we use the estimate:
x(+/-) z(α/2)(σ/√n)
At 99% Confidence interval means significance level is α=1-0.99= 0.01
So,
α/2=0.005
Now, z at α/2=0.005
z= 2.576
Now, by putting values
107(+/-)((2.576)(11.7/√84))
( 107-((2.576)(11.7/√84)), 107+((2.576)(11.7/√84)) )
(103.7, 110.288)
