1) You included neihter what Ramesh says nor the statements, then I can you tell some facts about the pattern.
2) The sequence is: 2401, 343, 49, 7, and 1.
3) The first term is 2401
4) The sequence is a decreasing geometric one.
5) The ratio is found dividing two consecutive terms (the second by the first, or the third by the second, or the fourth by the third, or the fifth by fourth):
1/7 = 7 / 49 = 49 / 343 = 343 / 2401.
So, the ratio is 1/7
6) The sum of that sequence is 2401 + 343 + 49 + 7 + 1 = 2801
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
Answer:
6 it is 6
Step-by-step explanation:
Answer:
60%
Step-by-step explanation:
percentage of men in the choir = (4/11) x 100 = 36.4%
percentage of women in the choir = (7/11) x 100 = 63.6%
Percentage of men in the choir that prefer classical songs = 36.4 x0.25 = 9.1%
Percentage of women in the choir that prefer classical songs = 0.8 x 63.6% = 50.9%
percentage of the choir prefer classical songs = 50.9% + 9.1% = 60%
75% of 56 is .75 * 56
.75 * 56 = 42
Because you are decreasing, you subtract 42 from 56.
56 - 42 = 14
A 75% decrease of 56 books would leave 14 books.
