Mathematics: The weight of an object is an example of: a. a discrete random variable. b. a continuous random variable. c. either a continuous or a discrete random variable, depending on the weight of the object. d. either a continuous or a discrete random variable depending on the units of measurement.

The weight of an object is an example of: a. a discrete

Ответ:

danielmartinez024m

16.03.2023

A sample size of 61 will produce a margin of error of 9% with 90% confidence level

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error of the confidence interval is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

p = 0.24

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.05$ , so Z = 1.645 .

What sample size will produce a margin of error of 9% with 90% confidence level

This is n when M = 0.09. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.645\sqrt{\frac{0.24*0.76}{n}}$

$0.09\sqrt{n} = 1.645\sqrt{0.24*0.76}$

$\sqrt{n} = \frac{1.645\sqrt{0.24*0.76}}{0.09}$

$(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.24*0.76}}{0.09})^{2}$

n = 61

A sample size of 61 will produce a margin of error of 9% with 90% confidence level

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The weight of an object is an example of: a. a discrete random variable. b. a continuous random variable. c. either a continuous or a discrete random variable, depending on the weight of the object. d. either a continuous or a discrete random variable depending on the units of measurement.

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