Answer:
The central line of the p-chart is 0.05.
Step-by-step explanation:
In statistical quality control, the p-chart is a form of control chart used to observe the proportion of non-conforming or defective components in a random sample, where the sample proportion of defective items is defined as the fraction of the number of defective units to the size of the sample, n.
The central line of the p-chart is given by:
[tex]CL=\frac{\sum np}{\sum n}[/tex]
It is provided that:
The sample selected from a shipment for inspection every day is of size, n = 50.
The average percentage of incorrect shipments is 5%, i.e. p = 0.05.
Compute the number defective units in the sample as follows:
[tex]np=50\times \frac{5}{100}[/tex]
Compute the central line of the p-chart as follows:
[tex]CL=\frac{\sum np}{\sum n}[/tex]
[tex]=\frac{5\times 50}{100\times 50}\\[/tex]
[tex]=0.05[/tex]
Thus, the central line of the p-chart is 0.05.
The center line for a p-chart is calculated as the average percentage of defects across all samples, which in this case is 5%.
The center line for a p-chart is calculated as the average percentage of defects across all samples.
In this case, the average percentage of incorrect shipments is 5%.
Hence, the center line for the p-chart in this scenario would be 5%.
A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypothesis below (versus a two-sided alternative) can be rejected?
A. H0: μd= 0.5B. H0: μd= 1.0C. H0: μd= 1.5D. H0: μd= 2.0
Answer:
Correct option is (A). H₀: [tex]\mu_{d}[/tex] = 0.5
Step-by-step explanation:
The (1 - α)% confidence interval for a population parameter can be used to determine whether to reject a null hypothesis or not.
The decision rule is:
If the (1 - α)% confidence interval for a population parameter consists of the null value of the parameter then the null hypothesis will be accepted or else it will be rejected.
A hypothesis test is performed to determine the difference between the ideal and actual heights of college males.
The 95% confidence interval for the mean difference, [tex]\mu_{d}[/tex] is:
CI = (0.8, 2.2)
The four null hypothesis provided are:
H₀: [tex]\mu_{d}[/tex] = 0.5H₀: [tex]\mu_{d}[/tex] = 1.0H₀: [tex]\mu_{d}[/tex] = 1.5H₀: [tex]\mu_{d}[/tex] = 2.0The 95% confidence interval for the mean difference consists of the value, 1.0, 1.5 and 2.0.
But it does not consist the value 0.5.
So, the null hypothesis that can be rejected is:
H₀: [tex]\mu_{d}[/tex] = 0.5
Thus, the correct option is (A).
Based on the 95% confidence interval given, we can only reject null hypothesis H0: μd= 0.5. The rest of the null hypotheses fall within the interval and therefore, cannot be rejected.
Explanation:Based on the 95% confidence interval, which ranges from 0.8" to 2.2", we are interested in whether 0 falls within this range. When it falls within this range, we cannot reject the null hypothesis. Going through the provided null hypotheses, we can reject the null hypothesis which falls outside the confidence interval.
Considering:
A. H0: μd= 0.5
B. H0: μd= 1.0
C. H0: μd= 1.5
D. H0: μd= 2.0
Only hypothesis A falls outside the confidence interval, thus we can reject null hypothesis H0: μd= 0.5. The null hypotheses stating μd= 1.0, μd= 1.5, and μd= 2.0 fall within this range and therefore, cannot be rejected based on this confidence interval.
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"D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours. Because of an improved production process, the company believes that there has been an INCREASE in the life expectancy of its D size batteries. A sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours. Conduct an appropriate hypothesis test. Find the t-statistic and the appropriate conclusion at the 0.1 level of significance.
Answer:
The calculated value t = 5.608 > 2.3988 at 0.1 level of significance with 53 degrees of freedom.
The null hypothesis is rejected at 0.1 level of significance
The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries
Step-by-step explanation:
Step(i):-
Given data the size of sample n=54
Given "D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours
therefore mean of Population μ = 85.5 hours
Given a sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours
The mean of the sample x⁻ = 88.7 hours
The standard deviation of the sample (S) = 3.8 hours
Step(ii):-
Null hypothesis : H₀:μ > 85.5 hours
Alternative hypothesis: H₁:μ < 85.5 hours
Level of significance : ∝= 0.1
Degrees of freedom γ =n-1 = 54-1 =53
The test statistic
[tex]t= \frac{x^{-}-u }{\frac{S}{\sqrt{n} } }=\frac{88.7-85.8}{\frac{3.8}{\sqrt{54} } }[/tex]
t = 5.608
The tabulated value t = 2.3988 at 0.1 level of significance with 53 degrees of freedom.
Conclusion:-
The calculated value t = 5.608 > 2.3988at 0.1 level of significance with 53 degrees of freedom.
The null hypothesis is rejected at 0.1 level of significance
The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries
What is the median of the numbers 4, 7, 15, 2, 9, 11
Step-by-step explanation:
Arranging in ascending order
2 , 4 , 7 , 9 , 11 , 15
No of data (N) = 6
Now
Position of median
= (N+1)/2 th item
= ( 6 + 1) /2 th item
= 7/2 th item
= 3.5 th item
Exact Median
= 3 + 0.5 ( 4th term - 3rd term)
= 3 + 0.5( 9 - 7)
= 3 + 0.5 * 2
= 3 + 1
= 4
Hope it will help :)
The results of a random survey show that 40 out of 75 people plan to vote for Mr.beston for a position on the local school board. Which is the best prediction of the number of people who will vote for Mr.beston if 3,000 people vote
Answer:
1,600
Step-by-step explanation:
3000/75=40
40*40=1,600
Final answer:
The best prediction for the number of people who will vote for Mr. Beston out of 3,000 voters is found through a simple proportion, resulting in an estimated 1,600 votes for Mr. Beston.
Explanation:
The question asks for a prediction of the number of people who will vote for Mr. Beston if 3,000 people vote, based on the results of a survey where 40 out of 75 people indicated they would vote for him. To find this prediction, we use a simple proportion. We set up a ratio of the number of people who plan to vote for Mr. Beston to the total number surveyed and set this equal to the unknown number of people who will vote for Mr. Beston out of 3,000 total voters.
The ratio or survey proportion is 40/75. We set up the following proportion to find the predicted number of votes:
40/75 = x/3000,
where x is the number we want to find. By cross-multiplying, we get:
40 * 3000 = 75 * x,
which simplifies to:
120,000 = 75x.
Now, we divide both sides by 75 to isolate x:
x = 120,000 / 75,
x = 1600.
Therefore, the best prediction is that 1,600 people out of 3,000 will vote for Mr. Beston.
U1.51.4
This excerpt mostly introduces
the character of King Henry, or Harry.
the setting of the port of Mars.
the conflict of a war between England and France.
the setting of the fields of war.
Answer: the character of king Henry, or Harry
Step-by-step explanation:
Jennifer started out with 8 dollars. Then she got some more money for her birthday she ended up with 15 dollars. How much did she get for her birthday
A 4-column table with 4 rows. The first column has no label with entries C, D, E, total. The second column is labeled A with entries X, Y, Z, 1.0. The third column is labeled B with entries 0.25, 0.68, 0.07, 1.0. The fourth column is labeled total with entries G, H, J, 1.0. Which value for Y in the table would be least likely to indicate an association between the variables? 0.06 0.24 0.69 1.0
Answer:
.69 or c
Step-by-step explanation:
A school sold tickets to a musical.
The school received
$6.50
$6.50
per ticket sold.
Write an equation that represents the relationship between the number of tickets sold and the total amount of money the school received from selling tickets.
Let
m=the money collected and
t= tickets sold.
m=6.50t
6.50 per ticket so you multiply 6.50 by t. The money collected is the answer to the equation. Hope this helps!
Eric spent $21.85, including sales tax, on 2 jerseys and 3 pairs of socks. The jerseys cost $6.75 each and the total sales tax was $1.03. Fill in the table with the correct prices.
Answer:
The socks cost $2.44 per pair
Step-by-step explanation:
Everything costs $21.85 in total. The given values are $6.75 for each jersey (which adds to make both jerseys together make $13.50). There is also a given value of $1.03 for total sales tax. If you add the jerseys and tax, you get $14.53. Subtract that from $21.85 to get $7.2. That is the total for all three pairs of socks, so divide that by three and you get $2.44 for each pair of socks :)
An angle is inscribed in a circle. The arc intercepted by this angle is 40°. What is the measure of the inscribed angle?
Answer:
20°
Step-by-step explanation:
Given:
Angle of Intercepted arc = 40°
If an angle is inscribed in a circle, the measure of the inscribed angle is half the measure of the intercepted arc.
Therefore, since the angle of Intercepted arc is 40°, the measure of inscribed angle will be:
[tex] \frac{1}{2} * 40 [/tex]
= 20
Answer:
the answer is 20 degrees
Step-by-step explanation:
just took it
State the complement of each of the following sets: (a) Engineers with less than 36 months of full-time employment. (b) Samples of cement blocks with compressive strength less than 6000 kilograms per square centimeter. (c) Measurements of the diameter of forged pistons that do not conform to engineering specifications. (d) Cholesterol levels that measure greater than 180 and less than 220.
Answer:
(a) Engineers with greater than 36 months of full-time employment.
(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter
(c) Measurements of the diameter of forged pistons that conform to engineering specifications.
(d) Cholesterol levels that measure less than 180 and greater than 220.
Step-by-step explanation:
The complement of a set refers to elements that does not exist in that set. It means what does not exist in the set but exist in the universal set.
(a) Engineers with greater than 36 months of full-time employment.
In this case, the Universal set is a set of engineers in full-time employment. The given set is for engineers with less than 36 months of full-time employment. The complement is engineers with greater than 36 months of full-time employment.
(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter
In this case, the universal set is a set of samples of cement block having compressive strength. The given set is a set of cement block having compressive strength less than 6000 kilograms per square centimeter. The complement is samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter.
(c) Measurements of the diameter of forged pistons that conform to engineering specifications.
In this case, the universal set is a set of measurements of the diameter of forged pistons. The given set is a set of measurements of the diameter of forged pistons that do not conform to engineering specifications. The complement is a set of measurements of the diameter of forged pistons that conforms to engineering specification.
(d) Cholesterol levels that measure less than 180 and greater than 220.
In this case, the universal set is a set of Cholesterol levels. The given set is Cholesterol levels that measure greater than 180 and less than 220. The complement is Cholesterol levels that measure less than 180 and greater than 220.
the complement sets are engineers with 36 months or more of full-time employment, samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more, measurements of the diameter of forged pistons that do conform to engineering specifications and cholesterol levels that measure 180 or less, or 220 or more.
Complement sets are those that are not a part of collection of set. For example, if a set contains the numbers from 1 to 5 and set a = {1, 3, 5} then complement of set A will have {2, 4}. Now applying this concept we get:
Engineers with less than 36 months of full-time employment: The complement set would be engineers with 36 months or more of full-time employment.Samples of cement blocks with compressive strength less than 6000 kilograms per square centimeter: The complement is samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more.Measurements of the diameter of forged pistons that do not conform to engineering specifications: The complement would be measurements of the diameter of forged pistons that do conform to engineering specifications.Cholesterol levels that measure greater than 180 and less than 220: The complement set would be cholesterol levels that measure 180 or less, or 220 or more.Thus, the complement sets are engineers with 36 months or more of full-time employment, samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more, measurements of the diameter of forged pistons that do conform to engineering specifications and cholesterol levels that measure 180 or less, or 220 or more.
What is the amplitude of the function ?
Answer:
3
Step-by-step explanation:
First, find the midline by averaging the highest value (2) and the lowest value (-4). In other words, do (2+-4)/2. You get the midline as -1. Now find the distance from the midline to the top. Distance from -1 to 2 is 3. Amplitude is therefore 3.
Final answer:
The amplitude of a function is represented by the symbol A, which is the maximum displacement from the equilibrium position in a sine wave function. The sinusoidal wave equation y(x) = Asin(ax) makes it clear that A is the amplitude.
Explanation:
The amplitude of a function, often represented by the symbol A, is the maximum displacement from the equilibrium position of an object oscillating around that equilibrium position. In the case of a sine function such as y(x) = Asin(ax), where x is the positional coordinate, the amplitude A is the distance from the equilibrium point to either the highest or lowest point of the wave. It is important to note that amplitude is different from peak-to-peak amplitude, which is the total vertical distance between the crest and the trough of a wave.
The equation provided, & (x) = Asin (ax), indicates that the function's amplitude is A. Specifically, for a sinusoidal wave like this, A represents the maximum vertical distance from the midpoint of the wave (equilibrium) to its crest (or trough).
how many times does 100 go into 540
Answer:
100 goes into 540 5 times
Step-by-step explanation:
which leaves a remainder of 40
hi and hope this helps!!
Answer:
5 remainder: 40 or 5.4
Step-by-step explanation:
when dividing 540 to 100, you need to know how many times 540 can go into 100. 100 can go into 540 5 times, so, you'll multiply 100 by 5. That should give you 500, then, you'll subtract 540 to 500, and that should give you a remainder of 40.
If you want to divide it to a decimal, you need to add an additional zero . to 40. That should give you 400. Then, 100 can go into 400, 4 times. So, you'll subtract 400 to 400, and that should give you 0. Now, you're done!
If you deposit $10,000 at 3.85% interest, compounded daily, what would your ending balance be after three years?
Answer: $11,155
Step-by-step explanation: For this problem, first we will use the "Simple Interest" equation to find the total interest earned after three years.
First, convert 3.85% to a decimal, 0.0385.
I, interest = 10,000 x 0.0385 x 3
I = 1,155
Now add the total interest $1,155 to the total deposit $10,000.
1,155 + 10,000 = $11,155
By using the formula for amount of Compound Interest the result is
Ending balance after 3 years = $11224.29
What is compound Interest?
If the interest on a certain principal increases exponentially rather than linearly on a certain rate over a certain period of time, then the interest obtained is known as compound interest.
If the principal be P, rate is r%, time is n years,
Amount = [tex]P(1 + \frac{r}{100})^n[/tex]
CI = Amount - Principal
Here,
Principal = $10000
Rate = 3.85%
Time = 3years
Amount =
[tex]10000(1+\frac{3.85}{36500})^{3\times 365}\\10000(1 + \frac{385}{3650000})^{1095}\\[/tex]
11224.29
Ending balance after 3 years = $11224.29
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The Polar Express movie is $12 and it will be on sale for $8.What is the percent of change
if the cost decreased $4?
please help
Answer:
33.333%.
Step-by-step explanation:
Take the cost changed ($4) and divide it by it's normal price ($12).
$4/$12 = .33333
Multiply that by 100 to get its percent. 33.333%
Answer:
- 33.3%
Step-by-step explanation:
You calculate percent change by dividing the change by the absolute value of the original. In this instance, it would be -4/12 which equals -0.3333. Multiply that by 100 and you get the percent.
A bag contains 6 red marbles, 9 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement.
Round your answers to 4 decimal places as needed.
1. What is the probability that all the marbles are red?
2. What is the probability that exactly two of the marbles are red?
3. What is the probability that none of the marbles are red?
Problem 1
Answer: 0.0002----------------
Work Shown:
There are n = 6 red marbles and r = 5 ways to pick them (order does not matter). Use the combination formula to find that
n C r = (n!)/(r!(n-r)!)
6 C 5 = (6!)/(5!*(6-5)!)
6 C 5 = (6!)/(5!*1!)
6 C 5 = (6*5!)/(5!*1!)
6 C 5 = (6)/(1!)
6 C 5 = (6)/(1)
6 C 5 = (6)/(1)
6 C 5 = 6
Now repeat for n = 6+9+8 = 23 and r = 5
n C r = (n!)/(r!(n-r)!)
23 C 5 = (23!)/(5!*(23-5)!)
23 C 5 = (23!)/(5!*18!)
23 C 5 = (23*22*21*20*19*18!)/(5!*18!)
23 C 5 = (23*22*21*20*19)/(5!)
23 C 5 = (23*22*21*20*19)/(5*4*3*2*1)
23 C 5 = (4037880)/(120)
23 C 5 = 33649
We have 6 ways of getting what we want (picking five red marbles) out of 33649 ways total (to get five marbles of any color). Again order does not matter.
Divide: 6/33649 = 0.00017831139112
This rounds to 0.0002 when rounding to four decimal places.
=========================================
Problem 2
Answer: 0.3031----------------
Work Shown:
There are 6 C 2 = 15 ways to pick 2 red marbles
There are 17 C 3 = 680 ways to pick 3 non-red marbles.
There are 15*680 = 10,200 ways to pick 5 marbles such that 2 are red, the rest aren't.
There are 33649 ways to select 5 marbles where color doesn't matter
So,
10200/33649 = 0.30312936491427
which rounds to 0.3031
=========================================
Problem 3
Answer: 0.1839----------------
Work Shown:
There are 17 marbles that aren't red, so there are 17 C 5 = 6188 ways to pull out five of them
This is out of 33649 ways to pull out five marbles in general.
6188/33649 = 0.18389848138131
which rounds to 0.1839
The probability of drawing all marbles red is extremely low (0.0002), while the probability of drawing exactly two red marbles is much higher (0.2865). If no red marbles are drawn, the probability is 0.1839.
To solve these problems, we will use the basic principles of probability and combinations, since we are dealing with the probability of drawing marbles without replacement.
1. Probability that all marbles are red
We have a total of 23 marbles (6 red, 9 white, 8 blue). Since we're drawing 5 marbles without replacement, to get the probability that all marbles are red, we need to calculate the combinations of choosing 5 out of 6 red marbles and divide that by the combinations of choosing 5 out of all 23 marbles.
Probability = (⁶C₅) / (²³C₅) = 6/33649 = 0.0002
2. Probability that exactly two of the marbles are red
Here, we want two red marbles and the remaining three to be non-red (either white or blue). We calculate this by multiplying the combination of choosing 2 reds out of 6, 3 non-reds out of 17 (total marbles minus red marbles), and divide by the total combinations of choosing 5 out of 23.
Probability = (⁶C₂ × ¹⁷C₃) / (²³C₅) = (15 × 680) / 33649 = 0.2865
3. Probability that none of the marbles are red
To find the probability of drawing no red marbles, we only consider the white and blue ones, so we want all 5 to be from the 17 non-red marbles.
Probability = (¹⁷C₅) / (²³C₅) = 6188 / 33649 = 0.1839