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Ne4ueva [31]
3 years ago
14

A lightbulb manufacturer wants to estimate the total number of defective bulbs contained in all of the boxes shipped by the comp

any during the past week. Production personnel at this company have recorded the number of defective bulbs found in each of 50 randomly selected boxes shipped during the past week. These data are provided in the file P08_12.xlsx. Calculate a 95% confidence interval for the total number of defective bulbs contained in the 1000 boxes shipped by this company during the past week. Hint: Note that sample size is 50 and population size is 1000. The question is asking for a confidence interval for a total.

Mathematics
1 answer:
abruzzese [7]3 years ago
6 0

Answer: we are 95% confident that the total number of defective bulb

contained in the 1000 boxes shipped by this company is between 195.5 and 644.5

Step-by-step explanation:

The sample size n = 50

The population size N= 1000

The number of defective in the sample is 21.

Sample mean x bar= 21/50

=0.42

The standard deviation (sigma) is = 0.81

Calculating the confidence interval

By checking the attached picture below.

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−2x=x^2−6
Iteru [2.4K]

Step-by-step explanation:

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2

f(2) = 23 − 3×22 – 2×2 + 4 = −4

f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

f(4) = 43 − 3×42 – 2×4 + 4 = 12

f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:

x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.

x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

x = 1

x = 1 + Ö5

x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution

f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.

The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

x = 1

x = −2

x = 1 +

x = 1 −

Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.

6 0
3 years ago
Read 2 more answers
A grocery store sells an 18 ounce container of peanut butter for $3.28. What is the cost per ounce (unit price)?
AnnyKZ [126]
Here,
cost of 18 ounce container of peanut butter = $3.28
cost of 1 ounce container of peanut butter = $3.28/18
                                                                    =$0.182
7 0
3 years ago
Read 2 more answers
Help please<br><br> how many should I use
andre [41]

Answer:

you should put 6 because 3/8 X 6 =18/8=2 2/6

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Sarah and her friends pick 3 3/4 pints of blueberries after they ate some of the blueberries only 2 1/3 pints remain how many pi
scoundrel [369]

3 3/4  - 2 1/3

get a common denominator of 12

3 3/4 * 3/3 = 3 9/12

2 1/3 * 4/4 = 2 4/12

3 9/12 - 2 4/12=

1 5/12

Answer: they ate 1 5/12 pints

7 0
3 years ago
What is the domain and range of this function?<br> I’ll put Brainliest! :)
tatuchka [14]

Answer:

Step-by-step explanation:

The Domain of a function is the x value, and the Range of a function is the y value. For example, in the ordered pair (9,4) the Domain is 9, or the x value, and the Range is 4, or the y value. So to find the Domain and Range, write ordered pairs for each plotted point on your graph (the dot at the end of each line) and then go through and identify the Domain and Range from there. When you list them, write the numbers in numeric order from least to greatest. Hope this helps!

5 0
2 years ago
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