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2 years ago

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Mathematics

1 answer:

Gelneren [198K]2 years ago

6 0

Answer:

First differences means take the ordered pairs in increasing order for their x coordinates (assuming the x's go by ones), then subtract each y (except the last) from the y that comes after it. Keep doing that and you get the first differences. (The second differences would be what you get if you then subtract each of the first differences from the one that came after it (TMI probably but ...)

Say the points were (1,3), (2,7), (3,11) and (4,15). The first differences are

7-3 = 4

11-7 = 4

15 - 11 = 4 all 4. This would also be the slope. So that is the relationship - they are the same.

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3 years ago

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Answer:

P (within $6 of 4) = 0.9164

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

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 $s = \frac{\sigma}{\sqrt{n}}$ .

Mean of $139 and a standard deviation of $30.

This means that $\mu = 139, \sigma = 30$

Random sample of 75 households

This means that $n = 75, s = \frac{30}{\sqrt{75}} = 3.464$

75 > 30, which means that the sampling distribution is approximately normal.

Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will be within $6 of the population mean.

This is the pvalue of Z when X = 139 + 6 = 145 subtracted by the pvalue of Z when X = 139 - 6 = 133.

X = 145

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$