Mathematics, 04.11.2020 18:00 abby894927

A scientist claims that 4% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5%? Round your answer to four decimal places.

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Answer from: Sushmitarai9416

The probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% is 0.1151.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p\\\\$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

The sample size is, n = 553 > 30. Thus, the Central limit theorem is applicable in this case.

Compute the mean and standard deviation as follows:

$\mu_{\hat p}=p=0.04\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.04\times 0.96}{553}}=0.0083$

Compute the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% as follows:

$P(\hat p0.05)=P(\frac{\hat p-\mu_{\hat p}}{\sigm_{\hat p}}\frac{0.05-0.04}{0.0083})\\\\=P(Z1.20)\\\\=1-P(Z$

Thus, the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% is 0.1151.

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

For the first question the answer is a, for the second c, for the third d, for the 4th b, for the 5th a

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