Find the mode of the following data . 12,8,4,8,1,8,9,11,9,10,12,8
2 answers:
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Answer:
[0.7210,0.8189] = [72.10%, 81.89%]
Step-by-step explanation:
The sample size is
n = 200
the proportion is
p = 154/200 = 0.77
<em>Since both np ≥ 10 and n(1-p) ≥ 10 </em>
<em>We can approximate this discrete binomial distribution with the continuous Normal distribution. As the sample size is large enough, not applying the continuity correction factor makes no significant difference. </em>
The approximation would be to a Normal curve with this parameters:
<em>Mean </em>
p = 0.77
<em>Standard deviation </em>
The 90% confidence interval for the proportion would be then
where is the 10% critical value for the Normal N(0,1) distribution , this is a value such that the area under the N(0,1) curve outside the interval
is 10%=0.1
We can either use a table, a calculator or a spreadsheet to get this value.
In Excel or OpenOffice Calc we use the function
<em>NORMSINV(0.95) and we get a value of 1.645 </em>
The 90% confidence interval for the proportion is then
This means there is a 90% probability that the proportion of people who watch educational television is between 72.10% and 81.89%
If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence interval?
Yes, I do.
Answer:
Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.
Step-by-step explanation:
Given that, a homeowner plans to enclose a 200 square foot rectangle playground.
Let the width of the playground be y and the length of the playground be x which is the side along the boundary.
The perimeter of the playground is = 2(length +width)
=2(x+y) foot
The material costs $1 per foot.
Therefore total cost to give boundary of the play ground
=$[ 2(x+y)×1]
=$[2(x+y)]
But the neighbor will play one third of the side x foot.
So the neighbor will play
Now homeowner's total cost for the material is
where C(x) is total cost of material in $.
Given that the area of the playground is 200.
We know that,
The area of a rectangle is =length×width
=xy square foot
∴xy=200
Putting the value of y in C(x)
The domain of C is.
Differentiating with respect to x
Again differentiating with respect to x
To find the critical point set C'(x)=0
Therefore
Therefore at x= 15.5 , C(x) is minimum.
Putting the value of x in we get
=12.9
Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.