Which amount is bigger 8/9 or .70

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on con

AlladinOne [14]

Using the z-distribution, a sample size of 180 is needed for the estimate.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is given by:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

In this problem, we have a 98% confidence level, hence $\alpha = 0.98$ , z is the value of Z that has a p-value of $\frac{1+0.98}{2} = 0.99$ , so the critical value is z = 2.327.

The population standard deviation is of $\sigma = 23$ , and to find the sample size, we have to solve for n when M = 4.

Hence:

$M = z\frac{\sigma}{\sqrt{n}}$

$4 = 2.327\frac{23}{\sqrt{n}}$

$4\sqrt{n} = 2.327 \times 23$

$\sqrt{n} = \frac{2.327 \times 23}{4}$

$(\sqrt{n}) = \left(\frac{2.327 \times 23}{4}\right)^2$

n = 179.03.

Rounding up, as a sample size of 179 would result in an error slightly above 4, a sample of 180 is needed.

More can be learned about the z-distribution at brainly.com/question/25890103

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8 0

1 year ago

Use properties of shapes and angles to find the missing measures.

guapka [62]

Answer:

< 1 = 130°, < 2 =50°, < 3 = 50°, < 4= 30°, < 5 = 70°, < 6 = 50°, < 7= 60°, < 8 = 40°, < 9 = 40°, < 10 = 50°, < 11 = 50°, < 12 = 130°, < 13 = 140°, < 14 =40° , < 15 = 140°

Step-by-step explanation:

< 4 = 90- 60 = 30° because angle 4 and angle 60° are complementary

< 5 = 70°, because vertical angles are congruent

< 2 = 180-130 = 50 °, because 130 ° and 2 are a linear pair

< 6 = 180-130 = 50 °, because 130 ° and 2 are a linear pair

because < 2 = < 6 and are alternate exterior angles then two lines are parallel

<13 = 140°, corresponding angles

< 13 = < 15 = 140°, vertical angles

< 8 = < 9 = < 14 = 180-140 = 40°, linear pair and vertical angles

< 3 = 180-90-40= 50 °, because the sum off all angles in a Δ is 180°

< 3= < 10 = < 11 =50° vertical angles , and corresponding angles

< 7= 180 -70 -50 = 60°, because the sum off all angles in a Δ is 180°