Mathematics, 15.06.2021 08:10 autumnxng3094

Suppose 54% of the registered voters in a country are Democrats. If a sample of 770 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 52%? Round your answer to four decimal places.

Answers: 2

Show answers

Answers

Answer from: jordan7626

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Step-by-step explanation:

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

Normal Probability Distribution:

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

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 $s = \sqrt{\frac{p(1-p)}{n}}$

Suppose 54% of the registered voters in a country are Democrats. Sample of 770.

This means that:

$p = 0.54, s = \sqrt{\frac{0.54*0.46}{770}} = 0.01796$

What is the probability that the sample proportion of Democrats will be greater than 52%?

This is 1 subtracted by the p-value of Z when X = 0.52. So

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

By the Central Limit Theorem

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

$Z = \frac{0.52 - 0.54}{0.01796}$

Z = -1.11

Z = -1.11 has a p-value of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Answer from: Quest

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

Answer from: Quest

go hook jvc hgv cj xk jvc 6756

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Adifferent website gives the cost for the first train as £56.88 and the second train as £20.11 with a £9.50 charge for cycle storage for the whole trip. how much would the journey cost you?

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Which value would be a solution for x in the inequality 47-4x< 7

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution

Answers: 2

Answer

Mathematics, 21.06.2019 23:40

What is the slope of (0,32) and (100,212)

Answers: 2

Answer

You know the right answer?

Suppose 54% of the registered voters in a country are Democrats. If a sample of 770 voters is select...

Questions