Mathematics, 09.03.2020 21:08 Alan0201

Use the Central Limit Theorem to find the indicated probability. The sample size is n, the population proportion is p, and the sample proportion is .
n = 160, p = 0.29; P( > 0.3)

Answers: 3

Show answers

Answers

Answer from: rubend661

P(X > 0.3) = 0.3897

Step-by-step explanation:

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

Applying the central limit theorem:

$\mu = p = 0.29, s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.29*0.71}{160}} = 0.0359$

P( > 0.3)

This is 1 subtracted by the pvalue of Z when X = 0.3. So

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

By the Central Limit Theorem

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

$Z = \frac{0.3 - 0.29}{0.0359}$

Z = 0.28

Z = 0.28 has a pvalue of 0.6103

1 - 0.6103 = 0.3897

P(X > 0.3) = 0.3897

Answer from: Quest

It equals 1373.5 that’s the solution

Answer from: Quest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

Another question on Mathematics

Mathematics, 21.06.2019 17:40

An apartment has a replacement cost of $950,000 and contents valued at $1,450,000. it has a classification of a and a territory rating of 3. find the annual premium a) $10,185 b) $9,230 c) $3,155 d) $13,830

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

Select the margin of error that corresponds to the sample mean that corresponds to each population: a population mean of 25, a standard deviation of 2.5, and margin of error of 5%

Answers: 2

Answer

Mathematics, 21.06.2019 20:10

Read the excerpt from the strange case of dr jekyll and mr. hyde what do dr. jekyll's thoughts reveal about him in this excerpt? [t]he inmates of my house were locked in the most rigorous hours of slumber, and i determined, flushed as i was with hope and triumph, to venture in my new shape as far as to my bedroom. i crossed the yard, wherein the constellations looked down upon me, i could have thought, with wonder, the first creature of that sort that their unsleeping vigilance had yet disclosed to he is jealous of those who can sleep through the night. he is revered for his scientific advances. he is interested in studying the movements of the stars he is proud and enthusiastic about his initial results.

Answers: 3

Answer

Mathematics, 21.06.2019 21:10

Aplane intersects a pris paralel to the base of the prism. the cross section is a polygon wth eight sides. how many sides does the base of the prism have? a. 10 b. 8 c. 7 d. 9

Answers: 1

Answer

You know the right answer?

Use the Central Limit Theorem to find the indicated probability. The sample size is n, the populatio...

Questions