Question

Find the truth set of each of these predicates where the
domain is the set of integers.
a) P(x): x3 ≥ 1 b) Q(x): x2 = 2
c) R(x): x < x2

Answer 1

Answer on Question #75826 – Math – Statistics and Probability

Question

Editors of the business report in Exercise 38 are willing to accept a margin of error of 4% but want 99% confidence. How many randomly selected employers will they need to contact?

Solution

Choose sample size for a given margin of error and confidence interval

$$ME = z_{\alpha/2} \sqrt{\frac{pq}{n}}$$

Solve the equation for $n$

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

$p = 0.5$ (because not mentioned anywhere)

$q = 1 - p = 0.5$

$ME = 4\%$

$$n = \frac{(2.576)^2 (0.5) (0.5)}{(0.04)^2} \approx 1037$$

Answer: 1037 employers.

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