Mathematics, 26.06.2020 16:01 u8p4

According to the Bureau of Labor Statistics, 7.1% of the labor force in Wenatchee, Washington was unemployed in February 2019. A random sample of 100 employable adults in Wenatchee, Washington was selected. Using the normal approximation to the binomial distribution, what is the probability that 6 or more people from this sample are unemployed

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Answer from: dreamdancekay

73.24% probability that 6 or more people from this sample are unemployed

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 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 = 100, p = 0.071

$\mu = E(X) = np = 10*0.071 = 7.1$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.071*0.929} = 2.5682$

What is the probability that 6 or more people from this sample are unemployed

Using continuity correction, this is $P(X \geq 6 - 0.5) = P(X \geq 5.5)$ , which is 1 subtracted by the pvalue of Z when X = 5.5. So

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

$Z = \frac{5.5 - 7.1}{2.5682}$

Z = -0.62

Z = -0.62 has a pvalue of 0.2676

1 - 0.2676 = 0.7324

73.24% probability that 6 or more people from this sample are unemployed

Answer from: Quest

a ≈ 172.05

step-by-step explanation:

the pictures.

Find the area of the regular pentagon. round decimal to the nearest

Answer from: Quest

step-by-step explanation:

hihi so drawing these 2 triangles is fairly simple. all that's left is finding the height of each one. luckily, we have a side length and an angle, so there is a trig function we can use to solve for the height. the easiest one to use would be tangent, since we have 2/3 things needed to find and the third needed is what we are solving for. tan(73°) * 30 ~= 98.13 and tan(73°) * 35 ~= 114.45

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