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:
x < 25
Step-by-step explanation:
Answer:
<u>Part A</u>

Applying Distributive property: 
<u>Part B</u>

Step-by-step explanation:
<em><u> Attached is the model that belongs to this exercise (The model was missing)</u></em>
The formula for calculate the area of a rectangle is:

Where "l" is the lenght and "w" is the width.
<u>Part A</u>
Notice that the dimensions of the new bathroom are:

We do not know the width of the new bathroom, but we know that both rooms will have the same length. Knowing this, we can write an expression for the total area of both rooms by using the Distributive Property:

Applying Distributive property:
<u>Part B</u>
If the width of the bedroom is 18 feet, you need to substitute this value into the expression
in order to find the total square footage of the two rooms:

Answer:
z³ = 64
z³=4³
since power is equal, base will be same
z=4
Step-by-step explanation: