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cupoosta [38]
2 years ago
8

An electronic device factory is studying the length of life of the electronic components they produced. The manager selects two

assembly lines and takes all samples on those two lines. He got a sample of 500 electronic components and records the length of life in the life test. A histogram indicates that the lifespans have moderate right skew. From the sample he found the average length of life was 200,000 hours and that the standard deviation was 1,000 hours. He wants to find the confidence interval for the average length of life of the electronic components they produced. Based on the information, what advice will you give to him
Mathematics
1 answer:
Temka [501]2 years ago
3 0

Answer:

The confidence interval will be given by:

200000 \pm 44.72z, in which z is related to the confidence level.

For a confidence level of x%, z is the value in the z-table that has a pvalue of 1 - \frac{1 - z}{2}

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In the context of this problems:

It means that the sampling distributions of the sample mean of 500 components will be approximated normal, with mean 200,000 and standard deviation s = \frac{1000}{\sqrt{500}} = 44.72

To build the confidence interval:

The confidence interval for the average length of life of the electronic components they produced will be given by:

200000 \pm 44.72z, in which z is related to the confidence level.

For a confidence level of x%, z is the value in the z-table that has a pvalue of 1 - \frac{1 - z}{2}

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kirill115 [55]
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 First by breaking down the numbers:
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4 0
2 years ago
The ratio of black marbles to red marbles is 3:2. If there are a total of 25 marbles in a bag,
kumpel [21]

Answer:

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Step-by-step explanation:

So its. A ratio (basically a fraction)

3/2

we add them up so we know how much marbles but not which kind

so we get 5

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so we divide 25/5 to get 5

now we know there are 5, 5 batches of black ad red marbles.

now black is 3 of them so we multiply 5(3) which is 15

Now red is 2 of them so we multiply 5(2). Which is 10

now to check, if we add them up, they equal to 25 which is correct.

basically add the fraction, divide that by the original number, time the quotient by each number in the fraction.

8 0
3 years ago
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tresset_1 [31]

Answer:

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Step-by-step explanation:

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The twenty-second term of (x+y)^25 is given by the binomial theorem as

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The coefficient required is therefore 12650, for a binomial with unit valued coefficients.

For other binomials, substitute the values for x and y and expand accordingly.

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