Mathematics, 09.04.2021 01:50 zahraa244

Consider the probability that no less than 95 out of 152 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

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Answer from: mncampbell01

0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Assume the probability that a given registered voter will vote in the presidential election is 61%.

This means that p = 0.61

152 registed voters:

This means that n = 152

Mean and Standard deviation:

$\mu = E(X) = 152*0.61 = 92.72$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{152*0.61*0.39} = 6.01$

Probability that no less than 95 out of 152 registered voters will vote in the presidential election.

This is, using continuity correction, $P(X \geq 95 - 0.5) = P(X \geq 94.5)$ , which is 1 subtracted by the pvalue of Z when X = 94.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{94.5 - 92.72}{6.01}$

Z = 0.3

Z = 0.3 has a pvalue of 0.6179

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.

Answer from: Quest

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1

What is the equation of the following line? be sure to scroll down first to see all answers options

Answer from: Quest

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.

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