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3 years ago

Really need help ?????pls

Mathematics

1 answer:

stealth61 [152]3 years ago

3 0

Answer:

34,833.21 ft³

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius

h is the height

Given

height h = 19 3/4 ft

d = 1 1/5h

d = 6/5 * h

d = 6/5 * 19 3/4

d = 6/5 * 79/4

d = 474/20

radius r = 474/20 * 1/2

radius r = 474/40

radus r = 11 34/40

radus r = 11 17/20 ft

Get the volume

V = 3.14 * (474/40)² * 79/4

V = 3.14 * 561.69 * 19.75

V = 34,833.20535

Hence the volume of the cylinder to the nearest hundredth is 34,833.21 ft³

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We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

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(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

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So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

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$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

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3 years ago