Answer:
Step-by-step explanation:
The associative property is helpful while adding or multiplying multiple numbers. By grouping, we can create smaller components to solve. It makes the calculations of addition or multiplication of multiple numbers easier and faster. Here, adding 17 and 3 gives 20.
the identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number.
what is factored form of x2-12x-4?
Answer:
The expression is not factorable with rational numbers...
Step-by-step explanation:
You are a personnel director and are interested in predicting the Number of Shares of Company Stock (Y) using the Number of Years Employed with the Company (X). You randomly selected 8 employees and found that the average number of shares is 525 and the average number of years employed is 22.5. If the slope (b1) is 20.0, what is the least squares estimate of the intercept (b0)
Answer:
intercept=b0=75
Step-by-step explanation:
The least squares estimate of the intercept b0 can be computed as
b0=ybar-b1*xbar.
ybar=average number of shares of company stock=525.
xbar= average number of years employed=22.5.
slope=b1=20.
Thus,
intercept=b0=ybar-b1*xbar
intercept=b0=525-20*22.5
intercept=b0=525-450
intercept=b0=75.
Thus, the estimate of intercept b0=75.
The mean salary of people living in a certain city is $37,500 with a standard deviation of $2,119. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income.
Answer:
The smallest sample size needed is 49.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income.
This is n for which [tex]M = 500, \sigma = 2119[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]500 = 1.645*\frac{2119}{\sqrt{n}}[/tex]
[tex]500\sqrt{n} = 1.645*2119[/tex]
[tex]\sqrt{n} = \frac{1.645*2119}{500}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*2119}{500})^{2}[/tex]
[tex]n = 48.6[/tex]
Rounding up
The smallest sample size needed is 49.
Answer:
[tex]n=(\frac{1.640(2119)}{500})^2 =48.31 \approx 49[/tex]
So the answer for this case would be n=49 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=37500[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=2119[/tex] represent the sample standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =500 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got [tex]z_{\alpha/2}=1.640[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.640(2119)}{500})^2 =48.31 \approx 49[/tex]
So the answer for this case would be n=49 rounded up to the nearest integer
What is/are the factor(s) in the "Sub-U-Like" study?
A. 30-second, 60-second and 90-second commercials
B. The number of students
C. Craving for Sub-U-Like
D. The length of the television program
E. Length and frequency of the commercial.
F. One, three, or five commercials during the 50-minute television program
Answer:
E. Length and frequency of the commercial.
Remaining Details of the Question:
A study investigated the effect of the length and the repetition of TV advertisements on students' desire to eat at a Sub-U-Like sandwich franchise. Sixty students watched a 50- minute television program that showed at least one commercial for Sub-U-Like during advertisement breaks. Some students saw a 30-second commerical, some saw a 60-second commercial, others a 90-second commerical. The same commerical was shown one, three, or five times during the program. After the viewing, each student was asked to rate their craving for a Sub-U-Like sandwich from the set ("Don't want to eat", "Neutral", "Want to eat"}
Explanation:
During the course of an experimental study, it is important to identify the variables of interest. These variables are referred to as the factors. Factors are controlled independent variables in an experimental study that can be manipulated by the experimenter.
In this case, it was indicated that the study investigated the effect of the length and the repetition of TV advertisements on students' desire to eat at a Sub-U-Like sandwich franchise. Therefore, the factors in the "Sub-U-Like" study are length and frequency of the commercial.
Final answer:
The factors in the "Sub-U-Like" study include the length and frequency of the commercial, the number of students, and the number of commercials during the TV program. Factors in the "Sub-U-Like" study, while not explicitly defined in the examples provided, can generally include variables such as length and frequency of commercials and the number of commercials shown, all of which can influence viewers' behaviors and perceptions in psychological or marketing research.
Explanation:
Factors in the "Sub-U-Like" study:
Factor A: Length and frequency of the commercial
Factor B: The number of students
Factor F: One, three, or five commercials during the 50-minute television program
Basic Computation: Setting Hypotheses Suppose you want to test the claim that a population mean equals 30 .
(a) State the null hypothesis. ___________________________
(b) State the alternate hypothesis if you have no information regarding how the population mean might differ from 30. _________________
(c) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be greater than 30. _______________
(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may not be as large as 30. ______________
Answer:
Part a
Null hypothesis: [tex]\mu =30[/tex]
Part b
Alternative hypothesis: [tex]\mu \neq 30[/tex]
Part c
Alternative hypothesis: [tex]\mu > 30[/tex]
Part d
Alternative hypothesis: [tex]\mu < 30[/tex]
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Solution to the problem
For this case we want to test if the true mean is equal to 30 or no.
Part a
Null hypothesis: [tex]\mu =30[/tex]
Part b
Alternative hypothesis: [tex]\mu \neq 30[/tex]
Part c
Alternative hypothesis: [tex]\mu > 30[/tex]
Part d
Alternative hypothesis: [tex]\mu < 30[/tex]
Solve the following:
1)If 32x=2, find x
2) simplify 9-1\2
Answer:
the answers are
1) 1/16
2) -18
Answer:
[tex]1)32x = 2 \\ \frac{32x}{32} = \frac{2}{32} \\ x = \frac{1}{16} [/tex]
[tex]2)9 - \frac{1}{2} \\ \frac{9}{1} \frac{ \times }{ \times } \frac{2}{2} - \frac{1}{2} \\ \frac{18}{2} - \frac{1}{2} \\ = \frac{17}{2} \\ = 8 \frac{1}{2} [/tex]
Given: ∠8 ≅ ∠16
Which lines must be parallel?
A) r and s
B) p and q
C) p and r
D) q and s
Hurry I need this one quick I don’t have a lot of time
Based on the converse of the Corresponding Angles Theorem, if ∠8 ≅ ∠16, then the lines that must be parallel are: A) r and s.
What is the converse of corresponding angles theorem?
If two lines are cut by a transversal, and the corresponding angles are congruent, then the lines are parallel, which is the converse of the Corresponding Angles Theorem.
In the image below, angles 8 and 16 are said to be congruent to each other, and both lie on lines r and s.
Therefore, based on the converse of the Corresponding Angles Theorem, lines r and s must be parallel (option A).
My computer is not letting me take a good quality of picture, but explanation and answer ?
Answer:
There will be 6 buses needed; the number of buses has to be a whole number.
Step-by-step explanation:
So we know that there is 232 people, and each bus holds 44 people. To find how many buses we need, you divide 232/44. Then, you get 5 with 12 extra. So you add one more bus, but that bus isn't full; there will only be 12 people inside it.
The reason why the number of buses has to be a whole number is because a bus has to be a whole bus, even though the bus isn't full. The maximum capacity of the bus is 44, but you can have 12 people inside it.
An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll an orange on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Answer:
Probability of an Orange on the next toss
= (23/60) = 0.3833
Step-by-step explanation:
Orange: 46
Brown: 23
Green: 32
Yellow: 19
Probability of an Orange on the next toss
= n(orange colours obtained in the tosses) ÷ n(number of tosses)
n(orange colours in the tosses) = 46
Total number of tosses = 46 + 23 + 32 + 19
= 120.
Probability of an Orange on the next toss
= (46/120) = (23/60) = 0.3833
Hope this Helps!!!!
The price-earnings (PE) ratios of a sample of stocks have a mean value of 10.5 and a standard deviation of 3. If the PE ratios have a normal distribution, use the Empirical Rule (also called the 68-95-99.7 Rule) to estimate the percentage of PE ratios that fall between:
Answer:
a) 68% falls within 7.5 and 13.5
b) 95% falls within 4.5 and 16.5
c) 99.7% falls within 1.5 and 19.5
Step-by-step explanation:
Given that:
mean (μ) = 10.5, Standard deviation (σ) = 3.
The Empirical Rule (also called the 68-95-99.7 Rule) for a normal distribution states that all data falls within three standard deviations. That is 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
Therefore using the empirical formula:
68% falls within the first standard deviation (µ ± σ) = (10.5 ± 3) = (7.5, 13.5)
95% within the first two standard deviations (µ ± 2σ) = (10.5 ± 2(3)) = (10.5 ± 6) = (4.5, 16.5)
99.7% within the first three standard deviations (µ ± 3σ) = (10.5 ± 3(3)) = (10.5 ± 9) = (1.5, 19.5)
inDJKL side JK measures 10.6 inches side KL measures 7 inches inside JL measures 5 inches based on the information that is provided which could be a correct set of angles measured for these sides?
angle J= 23.2 angle K equals 33.5 angle owl equals 23.2
angle J equals 23.2 angle K equals 33.5 angle L equals 123.2
angle J equals 123.2 angle K equals 23.2 angle L equals 33.5
angle J equals 33.5 angle K equals 23.2 angle L equals 123.2
Answer: Angle J = 33.5°, angle K = 23.2°, angle L = 123.2°
Step-by-step explanation: i did the quiz and got it correct :D
YAHOO!!! YOU ARE CORRECT!!! LETS GIVE HIM AROUND OF APPLAUSE!!!
So thats why its "angle J equals 33.5 angle K equals 23.2 angle L equals 123.2" is the last option! (D.) U R smart, Einstein! ;)
Christian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph
apart? Which of the following equations would you use to solve this word problem?
Answer:
65t+55t=540
Step-by-step explanation:
65 multiplied by four and a half equals 292.5
55 multiplied by four and a half equals 247.5
add together to get 540
If Christian travels north at 65 mph. The equations that you would use to solve this word problem is: 65t+55t=540.
Equation:The equation will be: 65t+55t=540
Where:
t=time
65=Distance to north per hour
55=Distance to south per hour
540=Miles apart
Therefore the equations that you would use to solve this word problem is: 65t+55t=540.
Learn more about equation here:https://brainly.com/question/2972832
#SPJ2
Factorize 12x² + 15xy
Answer:
[tex]12 {x}^{2} + 15xy \\ = 3x(4x +5 y)[/tex]
hope this helps you...
8x-y+3x what is the answer for that
Answer:
11x-y
Step-by-step explanation:
You add 8x+3x and get 11x then you put the equation together
11x-y
HOPE THIS HELPS!!!
We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20. At 95% confidence, the null hypothesis _____.
can someone help me with this
SurveyMonkey is a popular website for hosting online surveys and from time to time they will also create surveys based on a subject they are interested in answering questions about. Given the widespread adoption of dating sites and apps, they wanted to learn how people feel about them. It was found that out of 400 responses, 100 have used or are currently using online dating services. The average age of those that were using online dating services was 35 years old with a sample standard deviation of 12 years. What distribution should you use to compute a confidence interval for the average age of people using online dating services
Answer:
So we use the t-distribution to compute a confidence interval for the average age of people using online dating services
Step-by-step explanation:
Confidence interval for a mean.
We have to decide between the t-distribution and the z-distribution.
T-distribution: We use the sample standard deviation.
Z-distribution: We use the population standard deviation.
In this problem:
The average age of those that were using online dating services was 35 years old with a sample standard deviation of 12 years.
So we use the t-distribution to compute a confidence interval for the average age of people using online dating services
A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees high blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the blood pressure levels of the employees were measured again. Did the program reduce the average blood pressure level? The 95% confidence interval was (5.6, 10.2). What can we expect will be the p-value for a two sided test using this data? Group of answer choices The p-value should be smaller than 0.95 The p-value should be larger than 0.95 The p-value should be smaller than 0.05. The p-value should be higher than 0.05.
Answer:
The p-value should be smaller than 0.05.
Step-by-step explanation:
We know that the 95% confidence interval for the difference of means is (5.6, 10.2). As the lower bound is larger than 0, we are 95% confident that the reduction program had had a effect in the blood pressure level.
Then, as the program had a significant effect in the blood pressure level, we know that the null hypothesis (that states that the blood pressure levels would no change significantly) is then rejected.
If the significance level is 0.05, according to the confidence of the interval, to reject the null hypothesis, the p-value had to be lower than the significance level. In conclusion, the p-value should be lower than 0.05.
PLEASE HURRY NOW: Find the area of the rectangle below.
12 square units
24 square units
10 square units
20 square units
Convert 100 USD to rubles. Use exchange rate, where 1 USD equals 32.5 rubles.
Answer:
3250 rubles.
Step-by-step explanation:
1 USD = 32.5 rubles so...
1 * 100 USD = 32.5 * 100 rubles.
The answer is 3250 rubles.
Answer:
3250 rubles
Step-by-step explanation:
1 USD = 32.5 rubles
100 USD = 100 × 32.5
= 3250 rubles
7 divided by 4 long division
Write the equation of the line that goes through the point (-4,7) and has a slope of -5.
Answer:
y= -5x-13
Step-by-step explanation:
start with the linear equation
y= mx+b
indentify what you already have.
x= -4 and y= 7 and m(slope)= -5
We are solving for b, so plug in what you have.
7= -5(-4)+b
Simplify.
7= 20+b
Subtract 20 on both sides.
-13= b
Rewrite your equation with the x and y values.
y= -5x-13
Decompose 0.42 into tenths and hundredths
Answer:
0.40 + 0.02
Step-by-step explanation:
4 tenths plus 2 hundredths
Shawndra said that it is not possible to draw a trapezoid that is a rectangle, Explain your answer using the properties of quadrilaterals. Help FAST please. TELL ME WHAT TO DO AND SAY 30 points
Answer:
She is wrong
Rectangle can be a trapezoid
Step-by-step explanation:
A trapezoid is a quadrilateral which has atleast one pair of parallel sides.
A rectangle has two pairs of parallel sides, so it is a trapezoid too.
All rectangles are trapezoid.
But all trapezoids are not rectangles
A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?
Answer:
There is enough statistical evidence to support the claim that the survey is not accurate.
Step-by-step explanation:
We have to perform a test of hypothesis on the proportion.
The claim is that the proportion of families that own stock differs from 48.8%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.488\\\\H_a:\pi\neq0.488[/tex]
The significance level is 0.05.
The sample. of size n=250, has a proportion of p=0.568.
[tex]p=X/n=142/250=0.568[/tex]
The standard error of the proportion is
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.488*0.512}{250}}=\sqrt{0.00099}=0.032[/tex]
The z-statistic can now be calculated:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.568-0.488-0.5/250}{0.032}=\dfrac{0.078}{0.032}=2.4375[/tex]
The P-value for this two-tailed test is then:
[tex]P-value=2*P(z>2.4375)=0.015[/tex]
As the P-value is smaller than the significance level, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the survey is not accurate.
The suffecient eveidence to insure that the percentage of families who won stock is different from 48.8%.
Null Hypothesis:The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
The null hypothesis can be stated as shown below:
[tex]H_{0} :P=48.8[/tex]%
That is, the percentage of families who own stock is [tex]48.8[/tex]%.
The alternative hypothesis can be stated as shown below:
[tex]H_{a} :p\neq 48.8[/tex]%
That is, the percentage of families who own stock is different from [tex]48.8[/tex]%
The [tex]z[/tex] test statistic is given below:
[tex]z=\frac{\hat{p-p}}{\sqrt{\frac{p\left ( 1-p \right )}{n}}}[/tex]
Here, [tex]\hat{p}[/tex] is the observed proportion then, [tex]\hat{p}[/tex] is calculated by,
[tex]\hat{p}=\frac{x}{n} \\=\frac{142}{250} \\=0.568[/tex]
Therefore,
[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{p\left ( 1-p \right )}{n}}} \\=\frac{0.08}{0.0316}\\ =2.532[/tex]
Calculating the p-value be excel as attached below then we get,
The p-value is 0.01.
This p-value is called the actual level of significance.
The value of alpha is given as [tex]0.05[/tex]
Decision: The rejection of the null hypothesis [tex]H_0[/tex] because [tex]p-value < \alpha[/tex]
So, reject the null hypothesis.
Conclusion: The p-value is less than considered level of significance 5%.
Therefore the null hypothesis get rejected while the alternative hypotheisis is accepted.
Hence, there is suffecient eveidence to insure that the percentage of families who won stock is different from 48.8%.
Learn more about the topic Null Hypothesis:
https://brainly.com/question/24449949
Suppose the selling price of homes is skewed right with a mean of 350,000 and a standard deviation of 160000 If we record the selling price of 40 randomly selected US homes what will be the shape of the distribution of sample means what will be the mean of this distribution what will be the standard deviation of this distribution
Answer:
The distribution will be approximately normal, with mean 350,000 and standard deviation 25,298.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Suppose the selling price of homes is skewed right with a mean of 350,000 and a standard deviation of 160000
Sample of 40
Shape approximately normal
Mean 350000
Standard deviation [tex]s = \frac{160000}{\sqrt{40}} = 25298[/tex]
The distribution will be approximately normal, with mean 350,000 and standard deviation 25,298.
Answer:
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean would be:
[tex] \mu_{\bar X} =350000[/tex]
And the standard deviation would be:
[tex]\sigma_{\bar X} =\frac{160000}{\sqrt{40}}= 25298.221[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the selling price of a population, and for this case we know the following info
Where [tex]\mu=350000[/tex] and [tex]\sigma=160000[/tex]
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean would be:
[tex] \mu_{\bar X} =350000[/tex]
And the standard deviation would be:
[tex]\sigma_{\bar X} =\frac{160000}{\sqrt{40}}= 25298.221[/tex]
Which statements are true about a decagonal (10-sided) pyramid? Check all that apply.
It has one face that is a decagon.
It has two faces that are decagons.
It has 11 faces.
It has 20 edges.
It has 20 vertices.
Answer:
B. It has two faces that are decagons.
D. It has 20 edges.
E. It has 20 vertices.
Answer:b,d and e
Step-by-step explanation:
I think c is the right answer am I correct ?
Answer: yes
-5 is not greater than 4
-5
Step-by-step explanation:
"The Crunchy Potato Chip Company packages potato chips in a process designed for 10.0 ounces of chips with an upper specification limit of 10.5 ounces and a lower specification limit of 9.5 ounces. The packaging process results in bags with an average net weight of 9.8 ounces and a standard deviation of 0.12 ounces. The company wants to determine if the process is capable of meeting design specifications."
Answer:
The process does not meets the specifications.
Step-by-step explanation:
It is provided that the Crunchy Potato Chip Company packages potato chips in a process designed for 10.0 ounces of chips.
The value of upper specification limit is, USL = 10.5 ounces.
The value of lower specification limit is, LSL = 9.5 ounces.
The mean weight of the chips bags is, [tex]\bar X=9.8\ ounces[/tex].
And the standard deviation weight of the chips bags is, [tex]\sigma=0.12\ ounces[/tex].
Compute the value of process capability as follows:
[tex]C_{p_{k}}=min \{C_{p_{L}},\ C_{p_{U}}\}[/tex]
Compute the value of [tex]C_{p_{L}}[/tex] as follows:
[tex]C_{p_{L}}=\frac{\bar X-LSL}{3 \sigma}=\frac{9.8-9.5}{3\times 0.12}=0.833[/tex]
Compute the value of [tex]C_{p_{K}}[/tex] as follows:
[tex]C_{p_{K}}=\frac{USL-\bar X}{3 \sigma}=\frac{10.5-9.8}{3\times 0.12}=1.944[/tex]
The value of process capability is:
[tex]C_{p_{k}}=min \{C_{p_{L}},\ C_{p_{U}}\}[/tex]
[tex]=min\{0.833,\ 1.944\}\\=0.833[/tex]
The value of process capability lies in the interval 0 to 1. So the process is not capable of meeting design specifications.
Thus, the process does not meets the specifications.
Final answer:
The process capability of The Crunchy Potato Chip Company's packaging process has been questioned. By calculating the process capability index (Cpk), we find that the process capability is below the desirable threshold, suggesting that the process might not consistently meet the specified design requirements.
Explanation:
The student's query pertains to the process capability of The Crunchy Potato Chip Company's packaging process. This concept is part of quality control in process management and is measured by the process capability index (Cpk). In this case, the company has set specifications for a bag to contain between 9.5 and 10.5 ounces of chips and aims to have an average of 10.0 ounces. However, with a mean of 9.8 ounces and a standard deviation of 0.12 ounces, we need to calculate whether the process falls within the acceptable limits and how often it meets design specifications. To do this, the Cpk value is computed, which considers the mean, standard deviation, and the proximity of the mean to the closest specification limit.
Calculating the Process Capability Index (Cpk)
The formula for Cpk is:
Cpk = minimum of [(USL - mean) / (3 * sigma), (mean - LSL) / (3 * sigma)]
Where:
USL = Upper Specification Limit
LSL = Lower Specification Limit
mean = average net weight of the bags
sigma = standard deviation
Here, USL is 10.5 ounces, LSL is 9.5 ounces, mean is 9.8 ounces, and sigma is 0.12 ounces. Substituting these values:
Cpk = minimum of [(10.5 - 9.8) / (3 * 0.12), (9.8 - 9.5) / (3 * 0.12)]
Cpk = minimum of [1.9444, 0.8333]
The smaller of the two results is 0.8333, indicating that this is the Cpk value. A Cpk of 1.33 or higher is generally considered good, while a Cpk less than 1 indicates that the process may not be capable of meeting design specifications consistently. In this case, with a Cpk of 0.8333, The Crunchy Potato Chip Company's process may need improvement.
There are 157 college students interviewed about their work schedules. 85 of them work during the day. 43 of them work nightshift. 28 students work both. How many work old dayshift?
Step-by-step explanation:
No of students work during day shift = 85
No of students work during night shift = 43
No of students working both shift = 28
So first we will divide 28 by 2 = 14
Then it means there were 14 students working in day shift and 14 students working in night shift
Total number of students work during day shift = 85 + 14 = 99