Answer:
The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose a sample of 1536 floppy disks is drawn. Of these disks, 1383 were not defective.
1536 - 1383 = 153
This means that [tex]n = 1536, \pi = \frac{153}{1536} = 0.1[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 - 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.082[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 + 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.118[/tex]
The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).
please help me i’ll give brainliest
Answer:
105 degrees
Step-by-step explanation:
You need to understand the properties of corresponding angles and supplementary angles.
A young couple wants to save $40,000 over the next 5 years and then use this money as a down payment on a home. How much money must they deposit at the end of each quarter in an account that earns 5% compounded quarterly?
5% of 40,000 is 2,000
An investigator wishes to estimate the mean number of flight hours of pilots who fly for regional airlines. Assuming that the standard deviation of the number of hours is 120 hours, the minimum sample size needed in order to construct a 99% confidence interval for the mean number of hours of flight time of all such pilots, to within 50 hours, is about
Answer:
The minimum sample size needed is 39.
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 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
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.
Assuming that the standard deviation of the number of hours is 120 hour
This means that [tex]\sigma = 120[/tex]
The minimum sample size needed in order to construct a 99% confidence interval for the mean number of hours of flight time of all such pilots, to within 50 hours, is about?
The minimum sample size needed is n.
n is found when [tex]M = 50[/tex]
So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]50 = 2.575\frac{120}{\sqrt{n}}[/tex]
[tex]50\sqrt{n} = 2.575*120[/tex]
[tex]\sqrt{n} = \frac{2.575*120}{50}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*120}{50})^2[/tex]
[tex]n = 38.19[/tex]
Rounding up
The minimum sample size needed is 39.
solve the proportion for x. 12/x = 15/24
Answer:
i think x is 19.2
Step-by-step explanation:
solve x by cross multiplying
Help me answer these
Step-by-step explanation:
y=-2X2 -2X +4
Answer: I answered it it's C
1. What is your daily income if you earn $10.75/h as a camp counsellor and you work
10 hours per day?
I need help with these problem
9514 1404 393
Answer:
97,264.64 yd²
Step-by-step explanation:
The circumference of a sphere is the circumference of a circle with the same radius:
C = 2πr
The area of a sphere is given by the formula ...
A = 4πr²
In terms of circumference, that is ...
A = 4π(C/(2π))² = C²/π
Using the given values, the area of the sphere is ...
A = (552.64 yd)²/3.14 = 97,264.64 yd²
Answer:
97, 264.64 yd²Step-by-step explanation:
The circumference of a sphere is the circumference of the circle with the same radius:
C= 2πr
The area of a sphere is given by the formula...
A= 4πr²
In terms of circumference, that is...
A= 4π(C/(2π))²=C²/π
Using the given values, the area of the sphere is ...
A= (552.64 yd)²/3.14= 97, 264.64 yd²
Use the scale to find the actual area of Janets bedroom in square feet!
Answer: 17 feet long 14 feet wide
The model has a scale of 1 : 16 so you can use a calculator like this one to find the exact length. https://www.ginifab.com/feeds/cm_to_inch/scale_converter.html
Find the distance between A(4, —2) and B(—1, 2).
Round to the nearest tenth.
Answer:
6.4 to nearest tenth.
Step-by-step explanation:
AB = √[(x2 - x1)^2 + (y2-y1)^2]
= √[(-1 - 4)^2 + (2 - (-2))^2]
= √(25 + 16)
= 6.403
Find the value of x.
(a)
(10.7)" = 2
3x92x1 = 27*
(b)
Step-by-step explanation:
where is x in the question
id really appreciate it if someone helped me , i’ll give you brainliest
Answer: it’s the same 110 degrees
Step-by-step explanation:
Answer: 110 is the correct answer
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Please help me out here.............
Select the correct comparison
Answer:
b
Step-by-step explanation:
The quantity of a product demanded by consumers is a function of its price. The quantity of one product demanded may also depend on the price of other products. For example, if the only chocolate shop in town (a monopoly) sells milk and dark chocolates, the price it sets for each affects the demand of the other. The quantities demanded, q1​ and q2​, of two products depend on their prices, p1 and p2, as follows:
q1​=150−2p1​−p2
q2​=200−p1​−3p2​.​
If one manufacturer sells both products, how should the prices be set to generate the maximum possible revenue? What is that maximum possible revenue?
Answer:
Both prices should be set to #25.
The maximum revenue is #4375
Step-by-step explanation:
Given
[tex]q_1 = 150-2p_1-p_2[/tex]
[tex]q_2 = 200-p_1-3p_2[/tex]
Start by calculating the total revenue (R):
[tex]R = p_1q_1 + p_2q_2[/tex]
[tex]R = p_1(150-2p_1-p_2) + p_2(200-p_1-3p_2)[/tex]
[tex]R = 150p_1-2p_1^2-p_1p_2 + 200p_2-p_1p_2-3p_2^2[/tex]
Collect and solve like terms
[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]
Differentiate with respect to pi and to p2, respectively
[tex]\frac{dR}{dp_1} = 150 -4p_1 - 2p_2[/tex]
[tex]\frac{dR}{dp_2} = 200 -2p_1 - 6p_2[/tex]
Equate both to 0, to get the critical point
[tex]150 -4p_1 - 2p_2 = 0[/tex]
[tex]200 -2p_1 - 6p_2 = 0[/tex]
Solve for p1 in [tex]150 -4p_1 - 2p_2 = 0[/tex]
[tex]4p_1 = 150 - 2p_2[/tex]
[tex]p_1 = 37.5 - 0.5p_2[/tex]
Substitute [tex]p_1 = 37.5 - 0.5p_2[/tex] in [tex]200 -2p_1 - 6p_2 = 0[/tex]
[tex]200 - 2(37.5 - 0.5p_2) - 6p_2 = 0[/tex]
[tex]200 - 75 - p_2 - 6p_2 = 0[/tex]
[tex]125 - 7p_2 = 0[/tex]
[tex]-7p_2 =-125[/tex]
[tex]p_2 = 25[/tex]
Substitute [tex]p_2 = 25[/tex] in [tex]p_1 = 37.5 - 0.5p_2[/tex]
[tex]p_1 = 37.5 - 0.5 * 25[/tex]
[tex]p_1 = 37.5 - 12.5[/tex]
[tex]p_1 = 25[/tex]
So, we have:
[tex]p_1 = p_2 = 25[/tex]
This implies that the prices should be set to #25.
The maximum possible revenue is:
[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]
[tex]R = 150 * 25 + 200 * 25 -2 * 25^2 - 2 * 25 * 25 - 3 * 25^2[/tex]
[tex]R = 4375[/tex]
The maximum revenue is #4375
The maximum possible revenue is 4375.
How to calculate the revenue?From the information given, the following can be deduced:
Q₁ = 150 - 2P₁ - P₂
Q₁ = 150 - 2P₁ - P₂Q₂ = 200 - P₁ - 3P₂
The total revenue will be:
R = P₁Q₁+ P₂Q₂
R = P₁(150 - 2P₁ - P₂) + P₂(200 - P₁ - 3P₂)
R = 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²
To maximize, differentiate it in both the direction of P₁ and P₂.
d/dP₁ = 150 - 4P₁ - 2P₂
d/dP₂ = 200 - 2P₁ - 6P₂.
Solving for P₁ goes thus:
4P₁ = 150 - 2P₂
Divide through by 4
P₁ = 37.5 - 0.5P₂
Since 200 - 2P₁ - 6P₂ = 0
200 - 2(37.5 - 0.5P₂) - 6P₂ = 0.
P₂ = 25
Therefore, the revenue will be:
= 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²
= (150 × 25) + (200 × 25) - (2 × 25 × 25) - (3 × 25²)
= 4375
In conclusion, the revenue is 4375.
Learn more about revenue on:
https://brainly.com/question/25623677
Two consecutive integers have a product of 12. What is the initial equation that would be used
to solve this?
x² = 12
x(x + 1) = 12
2 (2+2) = 12
x(x − 2) = 12
Answer:
x(x+1) = 12
Step-by-step explanation:
If a number is x then it's consecutive number will be x + 1.
And their product x(x+1)
Multiply (2-5i)(2+5i)
Answer:
29
Step-by-step explanation:
4 - 25i^2
4 - 25x(-1)
4 + 25 = 29
the ^2 means exponent 2
Can someone please help me!!!
Classify the triangle as acute, obtuse, or right based on the given side
lengths. *
3,4,6
Acute
Obtuse
Right
Mr Soto bought some dvds each DVD cost 13.55 if Mr Soto did not spend more Thales 75$ which inequality could be used to find d the number of DVDs Mr. Soto bought
Answer:
c
Step-by-step explanation:
C is the only equality that no matter what, the value would be $75 or less
Walmart is selling
school supplies: 5
notebooks only cost
$4.02! How much
would znotebooks
cost? What about 7
notebooks?
Plz help! :)
Answer:
2 notebooks are $2.48, 7 notebooks are $8.68
Step-by-step explanation:
Unit rate is 1.24
1.24x2= $2.48
1.24x7= $8.68
Help me out
Answer required
Answer:
a. rational
b. irrational
c. irrational
d. rational
e. rational
f. rational
plz mark me as brainliest
[tex] 1)\displaystyle{} \: \sqrt{4} = \sqrt{2 \times 2} = \sqrt{2} \\ \: \: \: \bold{irrational \: number}[/tex]
[tex]2) \displaystyle{} \: \sqrt{3} = \bold{irrational \: number}[/tex]
[tex] \sqrt{7} \: \: = \bold{irrational \: number}[/tex]
[tex] 3) \: \: \displaystyle \frac{3}{5} \bold{irrational \: number}[/tex]
[tex] \displaystyle \: \frac{3}{5} \: \bold{rational \: number}[/tex]
[tex] \displaystyle{}\frac{1}{4} \bold{rational \: number}[/tex]
[tex] \displaystyle{} \: - 2.57 \: \bold{rational \: number}[/tex]
Note - if digit have root ( radical sign ) so number is irrational but digit have do not radical sign so number is rational.
What is integration of 3x^2
The probability that Ismael makes a basket is 7/10. If he shoots 100 baskets, how many can he expect to make?
Answer:
70 baskets
Step-by-step explanation:
Let b be the number of baskets he will make if he shoots 100 baskets.
[tex]\frac{7}{10} =\frac{b}{100} \\700=10b (now divide by 10 from both sides)\\[/tex]
This solid was created by joining two right rectangular prisms.
7 cm
9 cm
5 cm
4
4 / 3cm
12 cm
Enter the volume of the solid in cubic centimeters.
Answer: 648
Step-by-step explanation:
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3950 grams and a standard deviation of 374 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4473 grams. Round your answer to four decimal places.
Answer:
0.9192 = 91.92% probability that the weight will be less than 4473 grams.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Mean weight of 3950 grams and a standard deviation of 374 grams.
This means that [tex]\mu = 3950, \sigma = 374[/tex]
Find the probability that the weight will be less than 4473 grams.
This is the pvalue of Z when X = 4473. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4473 - 3950}{374}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a pvalue of 0.9192
0.9192 = 91.92% probability that the weight will be less than 4473 grams.
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
What is the measure of m?
6
m
18
n
m
=
[?]
Answer:
Step-by-step explanation:
the real answer is m=12:))
Help me to find the surface area pls :( :(
Answer:
154.521
Step-by-step explanation:
Have a good day!
Answer:
154.521
Step-by-step explanation:
The hypotenuse of a right triangle is 12.4 ft. One of the other two sides is 5.8 ft How
long is the third side?
