What is the sign of a.

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

Amy uses 20N of Force to push a lawn mower 10 meters how much does she do

navik [9.2K]

Work = Force * distance (along the line of force)
= 20N*10m
=200 N-m
=200 joules

6 0

3 years ago

What is the exact value of the trigonometric ratio of tan-240 degrees?

lara [203]

Tan240=1.732050808
Tan^-1(240)=89.76126897

8 0

3 years ago

Please help, I'm running out of points.

aksik [14]

Answer:

−5 < x < 10

Step-by-step explanation:

Add 1 to each part of the three parts of the inequality:

-6 +1 < x - 1 +1 < 9 +1

-5 < x < 10 . . . . . simplify

_____

The only place where there's an x is in the middle section. The only operation performed on x is subtraction of 1. To undo that subtraction, you add 1, but you must add 1 to all sides of the comparison symbols in order to keep them true.

Such a compound inequality is the same as the two inequalities:

-6 < x-1
x-1 < 9

Solving either one of these is done by adding 1 to both sides of the < symbol:

-5 < x
x < 10

You can put these back together in the form of the compound inequality ...

-5 < x < 10

3 0

3 years ago

Maria must give her dog 3 ml of ear drops medicine once per day in one ear for 3 days. The bottle contains 2 oz of medication Ex

Arte-miy333 [17]

Answer:

Step-by-step explanation:

5 0

3 years ago