Mathematics, 14.07.2020 23:01 reganjones89

In a survey of 1309 people, 825 people said they voted in a recent presidential election. Voting records show that 60% of eligible voters actually did vote. Given that 60% of eligible voters actually did vote, (a) find the probability that among 1309 randomly selected voters, at least 825 actually did vote.
(b) What do the results from part (a) suggest?

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Answer from: leeleegavin212

a) P(X>825)

b) This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.

Step-by-step explanation:

We know a priori that 60% of the eligible voters did vote.

From this proportion and a sample size n=1309, we can construct a normal distribution probabilty, that is the approximation of the binomial distribution for large samples.

Its mean and standard deviation are:

$\mu=n\cdot p=1309\cdot 0.6=785.4\\\\\sigma =\sqrt{np(1-p)}=\sqrt{1309\cdot 0.6\cdot 0.4}=\sqrt{314.16}=17.7$

Now, we have to calculate the probabilty that, in the sample of 1309 voters, at least 825 actually did vote. This is P(X>825).

This can be calculated using the z-score for X=825 for the sampling distribution we calculated prerviously:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{825-785.4}{17.7}=\dfrac{39.6}{17.7}=2.24\\\\\\P(X825)=P(z2.24)=0.0126$

This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.

Answer from: Quest

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule