Volume questionnnnnn

What is the surface area of the cube 64mm 192mm 384mm 512mm

Contact [7]

384 would be your answer. Hope this helps!

4 0

3 years ago

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production

Ghella [55]

Answer:

a) 0.3174 = 31.74% probability of a defect. The number of defects for a 1,000-unit production run is 317.

b) 0.0026 = 0.26% probability of a defect. The expected number of defects for a 1,000-unit production run is 26.

c) Less variation means that the values are closer to the mean, and farther from the limits, which means that more pieces will be within specifications.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Assume a production process produces items with a mean weight of 10 ounces.

This means that $\mu = 10$ .

Question a:

Process standard deviation of 0.15 means that $\sigma = 0.15$

Calculate the probability of a defect.

Less than 9.85 or more than 10.15. Since they are the same distance from the mean, these probabilities is the same, which means that we find 1 and multiply the result by 2.

Probability of less than 9.85.

pvalue of Z when X = 9.85. So

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

$Z = \frac{9.85 - 10}{0.15}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

2*0.1587 = 0.3174

0.3174 = 31.74% probability of a defect.

Calculate the expected number of defects for a 1,000-unit production run.

Multiplication of 1000 by the probability of a defect.

1000*0.3174 = 317.4

Rounding to the nearest integer,

The number of defects for a 1,000-unit production run is 317.

Question b:

Now we have that $\sigma = 0.05$

Probability of a defect:

Same logic as question a.

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

$Z = \frac{9.85 - 10}{0.05}$

$Z = -3$

$Z = -3$ has a pvalue of 0.0013

2*0.0013 = 0.0026

0.0026 = 0.26% probability of a defect.

Expected number of defects:

1000*0.0026 = 26

The expected number of defects for a 1,000-unit production run is 26.

(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

Less variation means that the values are closer to the mean, and farther from the limits, which means that more pieces will be within specifications.

3 0

3 years ago

Daniel rides his bicycle 21 km west and then 18 km north. How far is he from starting point

Inga [223]

The answer would be $\sqrt{765}$ or 27.7 km² if rounded to the nearest tenth

3 0

3 years ago

PLEASE EXPLAIN Find the area and perimeter of the rectangle whose sides are lengths 2x + 3 and 4x

SIZIF [17.4K]

Area = 4x(2x + 3) = 8x2 + 12x

Perimeter = 2(2x + 3 + 4x) = 12x + 6

4 0

3 years ago

Data collected over time on the utilization of a computer core (as a proportion of the total capacity) were found to possess a r

Marianna [84]

Answer:

The probability that the proportion of the core being used at any particular time will be less than 0.10 is 0.08146

Step-by-step explanation:

$\mu =\frac{\alpha }{\alpha +\beta } = \frac{1}{1 + \frac{\beta}{\alpha} }$ 1/3 0.33 = 33.33 %

The Probability of that the proportion of the core being used at any particular time will be less than 0.10 is given by

PDF = $\frac{x^{\alpha -1} (1-x)^{\beta -1} }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }$

where x = 0.1

α = 2 and β = 4

PDF = $\frac{0.0729 }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }$ = 1.458

CDF = $\frac{\int\limits^{0.1}_0 {t^{\alpha -1} (1-t)^{\beta -1}} \, du }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }$ = 0.08146

The probability that the proportion of the core being used at any particular time will be less than 0.10 = 0.08146.

3 0

4 years ago