A.) For n independent variates with the same
distribution, the standard deviation of their mean is the standard
deviation of an individual divided by the square root of the sample
size: i.e. s.d. (mean) = s.d. / sqrt(n)
Therefore, the standard deviation of of the average fill volume of 100 cans is given by 0.5 / sqrt(100) = 0.5 / 10 = 0.05
b.) In a normal distribution, P(X < x) is given by P(z < (x - mean) / s.d).
Thus, P(X < 12) = P(z < (12 - 12.1) / 0.05) = P(z < -2) = 1 - P(z < 2) = 1 - 0.97725 = 0.02275
c.) Let the required mean fill volume be u, then P(X < 12) = P(z < (12 - u) / 0.05) = 1 - P(z < (u - 12) / 0.05) = 0.005
P(z < (u - 12) / 0.05) = 1 - 0.005 = 0.995 = P(z < 2.575)
(u - 12) / 0.05 = 2.575
u - 12 = 2.575 x 0.05 = 0.12875
u = 12 + 0.12875 = 12.12875
Therefore, the mean fill volume should be 12.12875 so that the probability that the average of 100 cans is below 12 fluid ounces be 0.005.
d.) Let the required standard deviation of fill volume be s, then P(X < 12) = P(z <
(12 - 12.1) / s) = 1 - P(z < 0.1 / s) = 0.005
P(z < 0.1 / s) = 1 - 0.005 = 0.995 = P(z < 2.575)
0.1 / s = 2.575
s = 0.1 / 2.575 = 0.0388
Therefore, the standard deviation of fill volume should be 0.0388 so that the probability that the average of 100 cans is below 12 fluid ounces be 0.005.
e.) Let the required number of cans be n, then P(X < 12) = P(z <
(12 - 12.1) / (0.5/sqrt(n))) = 1 - P(z < (12.1 - 12) / (0.5/sqrt(n))) = 0.01
P(z < 0.1 / (0.5/sqrt(n))) = 1 - 0.01 = 0.99 = P(z < 2.327)
0.1 / (0.5/sqrt(n)) = 2.327
0.5/sqrt(n) = 0.1 / 2.327 = 0.0430
sqrt(n) = 0.5/0.0430 = 11.635
n = 11.635^2 = 135.37
Therefore, the number of cans that need to be measured such that the average fill volume is less than 12 fluid ounces be 0.01
If the perimeter of the equilateral triangle is 18 cm then the width of the rectangle be 11.2 cm.
Given that the perimeter of the equilateral triangle be 18 cm and the perimeter of all the three triangles be 46.4 cm.
We are required to find the width of the rectangle.
Rectangle is basically the shape which is having opposite sides equal to each other.
Perimeter of equilateral triangle=3 *side
3* side=18
side=18/3
side=6
Since it is on the length of the rectangle so the length of rectangle be
6 cm.
Perimeter of all the three triangles=2*width of the rectangle+1 length+perimeter of 1 equilateral triangle.
T1 and T2 are the other triangles.
Suppose the width of the rectangle be x.
Perimeter=2*x+6+18
46.4=2x+24
2x=46.4-24
2x=22.4
x=11.2
So,the width of the rectangle is equal to 11.2 cm.
Hence if the perimeter of the equilateral triangle is 18 cm then the width of the rectangle be 11.2 cm.
Learn more about perimeter at brainly.com/question/19819849
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100=1,478,300
1000=1,478,000
10,000=1,470,000
Answer:
61 is ur answer
Step-by-step explanation:
Since this was a 90 degree angle you would just subtract 29 from the 90 degrees and get your answer.
