In which quadrant is the number –14 – 5i located on the complex plane?

Mathematics

1 answer:

loris [4]3 years ago

5 0

Answer:

The complex number $r = -14 - i\,5$ belongs to the third quadrant of the complex plane.

Step-by-step explanation:

Let be $r = -14 - i\,5$ . In the complex plane, if $\Re (r) < 0$ (real component) and $\Im (r) < 0$ (imaginary component), the number belongs to the third quadrant of the complex plane. The complex number $r = -14 - i\,5$ belongs to the third quadrant of the complex plane.

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Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that

xxMikexx [17]

Answer:

99.36% probability that the sample proportion will differ from the population proportion by less than 6%

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 normally distributed samples are 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 $s = \frac{\sigma}{\sqrt{n}}$ .

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

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