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katrin2010 [14]
3 years ago
13

Write a general rule for adding

Mathematics
1 answer:
Elodia [21]3 years ago
3 0
<span>General rule for adding numbers
Two integers with the same signs
=> Once 2 integers has the same sign, then add.
For example
5 + 3 = 8 ( 5 and 3 are both positive numbers)
-5 + (-3) = -8 (5 and 3 are both negative number, thus we added the 2 numbers)

Two integers with different signs
=> When 2 integers has different sign, then do subtraction
For example
-5 + 3  (5 and 3 has different signs)
- 5 + 3 = 2

Two integers that vary in sign
=> When 2 integers vary in sign, then it will depend on the operator
For example
5 + (-3) (5 and 3 has different signs, but the process will vary with the operator and number sign)
When positive and negative = negative
5 – 3 = 2


</span>



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Answer:

a) 0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers

b) 0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers

c) 1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.

Step-by-step explanation:

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.

Standard deviation of 500 kilometers

This means that \sigma = 500

a. Assuming the mean is 1500 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

Mean of 1500 km means that \mu = 500

The probability is the pvalue of Z when X = 500. So

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

Z = \frac{500 - 1500}{500}

Z = -2

Z = -2 has a pvalue of 0.0228

0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers.

b. Assuming the mean is 1200 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

Now \mu = 1200

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

Z = \frac{500 - 1200}{500}

Z = -1.4

Z = -1.4 has a pvalue of 0.0808

0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers.

c. If, in fact, the northward displacement is less than 500 kilometers, which is the more plausible mean, 1200 or 1500 kilometers?

1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.

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