Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)

1 answer:

6 0

a) The empty set. b) The set can be represented in roster form as a comma-separated list. For instance, the natural numbers x that satisfy x + 4 = 1 describe an empty set. Thus, x represents an empty set. For part b, using set-builder notation, the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} can be expressed as: \{x | x is a natural number and x ≤ 12\}.

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An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation of all

Leona [12618]

Answer:

$n=(\frac{0.539(2.2)}{0.3})^2 =15.62 \approx 16$

In this scenario, the solution for n is determined to be 16 when rounded up to the closest integer

Step-by-step explanation:

The following information has been provided for this case:

$\sigma = 2.2$ symbolizes the population standard deviation

$Confidence =0.8$

$ME = 0.3$ signifies the preferred margin of error

The formula for the margin of error of the actual mean is given as:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

In this case, the margin of error (ME) is 0.03, and to find n, we rearrange equation (a) to get:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

With a confidence level of 80%, and the significance level being $\alpha=0.2$ and $\alpha/2 =0.1$ , the critical value is $z_{\alpha/2}=0.539$ . Plugging in these values into formula (b) results in: