5. Suppose that a particular candidate for public

Ответ:

201010399

26.06.2020

Probability that the sample proportion will be greater than 0.5 is 0.8133.

Step-by-step explanation:

We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.

Suppose that the polling organization takes a simple random sample of 500 voters.

Let $\hat p$ = sample proportion

The z-score probability distribution for sample proportion is given by;

Z = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion

p = population proportion = 48%

n = sample of voters = 500

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the sample proportion will be greater than 0.5 is given by = P( $\hat p$ > 0.50)

P( $\hat p$ > 0.50) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\frac{0.50-0.48}{\sqrt{\frac{0.50(1-0.50)}{500} } }$ ) = P(Z < 0.89) = 0.8133

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.

Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.

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Ответ:

clemsongirl5392

04.06.2021

Mathematics

answer: the volume of the sphere is 150 cm³

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from the diagram, we can see that

radius of sphere = radius of cylinder

height of cylinder = 2 · (radius of sphere)

the volume of the cylinder is given as 450 cm³.

formula for volume of cylinder:

$v_{\text{cylinder} } = \pi r^2 h$

we established before that the height of the cylinder is double the radius of the sphere. and since the radius of the sphere is the same as the radius of the cylinder, we can say that h = 2r:

$v_{\text{cylinder} } = \pi r^2(2r) = 2 \pi r^3$

using the fact that the volume of the cylinder is 450 cm³, we can solve for r

$\begin{aligned} 450 & = 2\pi r^3 \\ r^3 & = \frac{450}{2\pi} \\ r & = \sqrt[3]{\frac{225}{2\pi} } \end{aligned}$

the volume of a sphere is

$v_{\text{sphere } } = \dfrac{4}{3}\pi r^3$

using the radius we got from above, we calculate as follows:

$\begin{aligned} v_{\text{sphere } } & = \dfrac{4}{3}\pi \left( \sqrt[3]{\frac{225}{2\pi} } \right)^3 \\ & = \frac{4}{3}\pi \cdot \frac{225}{2\pi} \\ & = \frac{2}{1} \cdot \frac{75}{1} \\ & = 150\text{ cm}^3 \end{aligned}$

the volume of the sphere is 150 cm³

Asphere is just enclosed inside a right circular cylinder. if the volume of the cylinder is 450 cm3,

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