Mathematics, 13.02.2020 23:56 beluvangel418

A sample of 400 observations will be taken from an infinite population. The population proportion equals .8. The probability that the sample proportion will be greater than .83 is:

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Answer from: jossfajardo50

6.68% probability that the sample proportion will be greater than .83.

Step-by-step explanation:

We are going to approximate the binomial distribution to the normal.

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 samples 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

n = 400, p = 0.8

$\mu = E(X) = np = 400*0.8 = 320$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.8*0.2} = 8$

The probability that the sample proportion will be greater than .83 is:

83% of 400 is 0.83*400 = 332.

So this probability is 1 subtracted by the pvalue of Z when X = 332.

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

$Z = \frac{332 - 320}{8}$

Z = 1.5

Z = 1.5 has a pvalue of 0.9332.

So 1-0.9332 = 0.0668 = 6.68% probability that the sample proportion will be greater than .83.

Answer from: Quest

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2 is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes. our only condition is that it passes through the point (-2,5)

A. write an equation of a line that passes through (-2, 5). b. how many different equations could y

Answer from: Quest

i believe the answer is letter c) 8

step-by-step explanation:

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