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2 answers:
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Answer:
Surface area of square box cover is 4x12=48
Step-by-step explanation:
Given cylindrical cup have 2 in of radius and height of 6 in.
It is said that we need to cover the cup leaving top and bottom of cup.
To find how much material to cover:
After covering the cup, square box will be formed around the cup.
As shown in figure, Top view of square cup and box.
One face of box has length of diameter of cup = 2 in and height of box as height of cup = 6 in
Therefore, Area of one face of square box is length x height = 2 x 6 =12
Since, Box having 4 faces
Surface area of square box cover = 4 x area of one face of box
= 4x12=48
Answer:
a) P(-z_0.025 < Z < z_0.025)
For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(0.025,0,1)"
"=NORM.INV(0.025,0,1)"
And for this case the two values are :
b) P(-z_{\alpha/2} < Z < z_{\alpha/2})
For this case we want a quantile that accumulates of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(alpha/2,0,1)"
"=NORM.INV(alpha/2,0,1)"
c) For this case we want to find a value of z that satisfy:
P(Z > z_alpha) = 0.05.
And we can use the following excel code:
"=NORM.INV(0.95,0,1)"
And we got
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Part a
P(-z_0.025 < Z < z_0.025)
For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(0.025,0,1)"
"=NORM.INV(0.025,0,1)"
And for this case the two values are :
Part b
P(-z_{\alpha/2} < Z < z_{\alpha/2})
For this case we want a quantile that accumulates of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(alpha/2,0,1)"
"=NORM.INV(alpha/2,0,1)"
Part c
For this case we want to find a value of z that satisfy:
P(Z > z_alpha) = 0.05.
And we can use the following excel code:
"=NORM.INV(0.95,0,1)"
And we got
Since m is the midpoint of ab, then the following relationship is fulfilled:
Therefore, substituting values we have:
From here, we clear the value of x.
We have then:
Then, the value of am, is given by substituting x in the expression:
Substituting we have:
Answer:
the length of am is:
Therefore, substituting values we have:
From here, we clear the value of x.
We have then:
Then, the value of am, is given by substituting x in the expression:
Substituting we have:
Answer:
the length of am is: