Subtract 10 from each side to get -5m=35
Divide each side by -5 to get m=-7
So m=-7
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
It's a simple linear equation in a single variable, 'y' . Its solution is the number
that 'y' must be in order to make the equation a true statement. Here's how to
find the solution:
Write the equation: <span>15 = -y + 10
Subtract 10 from each side: 5 = -y
Multiply each side by -1 : <u>-5 = y</u>
</span>
Answer:
I'm confused too I'm sorry
Using the number line, the numbers that are 9 units from -5 are: -14 and 4.
<h3>How to Locate a Number on a Number line?</h3>
To find two numbers that cover the same units from a given point on a number line, we can simply do the following:
- Count the number of units given backwards/to the left from the point stated to get the first number.
- Count the number of units given forwards/to the right from the point stated to get the second number.
Thus, we are asked to find the numbers that would be 9 units from -5, using the number line.
Count 9 units backwards/to the left from -5 to get the first number, which is: -14
Count 9 units forwards/to the right from the -5 to get the second number, which is: 4.
Therefore, the numbers that are 9 units from -5 on the number line, are: -14 and 4.
Learn more about number line on:
brainly.com/question/24644930
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