Please help!! Worth 28 points if you can solve it correctly and proof on paper

Mathematics

1 answer:

OlgaM077 [116]4 years ago

3 0

8p + 3q - 18 when p = 1/2 and q = 7

You are given that p is equal to 1/2 and q is equal to 7, so plug these values into p and q in the expression to find your answer.

Rewrite your expression to include the values of p and q plugged in. Your expression should look like:

8(1/2) + 3(7) - 18

According to PEMDAS, multiplication should be solved first before doing subtraction, so multiply 8 by 1/2 and 3 by 7. Rewrite your expression; your expression should look like this:

4 + 21 - 18

According to PEMDAS, addition and subtraction should be solved from left to right; they are not prioritized. So solve the expression from left to right and then you will have your answer.

4 + 21 = 25

25 - 18 = 7

Your answer is 7.

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Answer:

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American.

This means that $p = 0.18, n = 100$