Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Soft-drink cans are filled by an automated filling machine and the standard deviation is 0.5 fluid ounces assume that the fill v

evablogger [386]

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

8 0

3 years ago

Find 0. Round to the nearest degree. A. 21° B. 20° C. 69° D. 70°

kap26 [50]

Answer:

B 20

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Write the equation for a parabola that has a vertex (2, -1) and a directrix of x = 5.

Alika [10]

The equation of the parabola that has a vertex (2 , -1) and a directrix

of x = 5 is (y + 1)² = -12(x - 2)

Step-by-step explanation:

Let us revise the equation of a parabola

1. The form of the equation is (y − k)² = 4p(x − h)

2. The coordinates of its vertex are (h , k)

3. The equation of its axis of symmetry is y = k

4. The coordinates of the focus are (h + p , k)

5. The directrix is at x = h − p

∵ The coordinates of the vertex of the parabola are (2 , -1)

∵ The coordinates of its vertex are (h , k)

∴ h = 2 and k = -1

∵ The directrix is at x = 5

∵ The directrix is at x = h − p

∴ h - p = 5

∵ h = 2

∴ 2 - p = 5

- Subtract 2 from both sides

∴ - p = 3

- Multiply both sides by -1

∴ p = -3

∵ The form of the equation is (y − k)² = 4p(x − h)

∴ (y - -1)² = 4(-3)(x - 2)

∴ (y + 1)² = -12(x - 2)

The equation of the parabola that has a vertex (2 , -1) and a directrix

of x = 5 is (y + 1)² = -12(x - 2)

Learn more:

You can learn more about equation of a parabola in brainly.com/question/8054589

#Learnwithbrainly

3 0

3 years ago

Read 2 more answers

Convert 10300000in scientific notation

insens350 [35]

Step-by-step explanation:

10300000 = 1,03 * 10⁷

3 0

4 years ago

Read 2 more answers

What is the quotient?

Ierofanga [76]

Answer:

3/2

Step-by-step explanation:

For dividing rational expressions such as the one given, we use the same concept that we use when dividing fractions.

Thus, we multiply the first expression with the second expression's reciprocal as shown below.

$\frac{2m + 4}{8} \div \frac{m + 2}{6}$

$\frac{2(m + 2)}{8} \times \frac{6}{m + 2}$

We can cancel common factors and simplify the product. Hence, we have

$\frac{2(6)}{8}$

$\frac{3}{2}$

Therefore, the quotient of the expressions is equal to 3/2.

6 0

2 years ago