Complete the problems. Show your work.

A manufacturer makes chocolate squares that have a target weight of 8 g. Quality control engineers sample 30 chocolate squares t

posledela

Using the normal distribution and the central limit theorem, it is found that the power of the test is of 0.9992 = 99.92%.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is $\mu = 8.5$ .

The standard deviation is $\sigma = 0.87$ .

A sample of 30 is taken, hence $n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588$ .

The power of the test is given by the probability of a sample mean above 8, which is 1 subtracted by the p-value of Z when X = 8, so:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem:

$Z = \frac{X - \mu}{s}$

$Z = \frac{8 - 8.5}{0.1588}$

$Z = -3.15$

$Z = -3.15$ has a p-value of 0.0008.

1 - 0.0008 = 0.9992.

The power of the test is of 0.9992 = 99.92%.

To learn more about the normal distribution and the central limit theorem, you can check brainly.com/question/24663213

5 0

3 years ago

A and B working together complete a work in 35 days. If A takes 60 days to complete it, how long would B alone tale to complete

svp [43]

Answer:

Efficiency (Work done per day) for :

( ˘ ³˘)/

A & B together = 1/35th

A alone = 1/60th

Thus, efficiency of B alone = Total - A’s efficiency

Step-by-step explanation:

OR Efficiency of B alone = (1/35) - (1/60) = 6/210 - 3.5/210 = 2.5/210 = 1/84th

Hence, since B completes 1/84th work daily, he would take 84 days to complete the work alone.

7 0

3 years ago

What is the blank answer?

Taya2010 [7]

Answer:

you.. need to provide a picture

Step-by-step explanation:

7 0

3 years ago

Order the real numbers from least to greatest use the < symbol. -16.34, 2 pi. 148/9. 16. -266 does anybody know the answer

denpristay [2]

-266 < -16.34 < 2pi < 16 < 148/9=16 4/9

7 0

4 years ago

Heyo random person scrolling.Please help me?

Ierofanga [76]

Let's do

$\\ \sf\longmapsto 2sin^260cos60tan^245$

$\\ \sf\longmapsto 2\left(\dfrac{\sqrt{3}}{2}\right)^2\times \dfrac{1}{2}\times (1)^2$

$\\ \sf\longmapsto 2\times \dfrac{(\sqrt{3})^2}{2^2}\times \dfrac{1}{2}\times 1$

$\\ \sf\longmapsto \dfrac{3}{2}\times \dfrac{1}{4}$

$\\ \sf\longmapsto \dfrac{3}{4}$

Trigonometric values

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \csc & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}}$

6 0

3 years ago