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Anuta_ua [19.1K]
3 years ago
7

A publisher requires 2⁄3 of a page of advertisements for every 5 pages in a magazine. If a magazine has 98 pages, to the nearest

whole page, how many pages of the magazine are advertisements?
Mathematics
1 answer:
Ivanshal [37]3 years ago
3 0

To solve this problem you must apply the proccedure shown below:

  1. You have \frac{2}{3} of a page of advertisements for every 5 pages in the magazine and the it has 98 pages. Therefore, you must multiply the total pages by 2/3 and divide the result by 5 pages.
  2. Then:

x: number of pages of the magazine are advertisements

x=\frac{(98)(\frac{2}{3}) }{5} \\ x=13

Therefore, the answer is: 13 pages.

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Answer:

The distance of the park from the Gary's house is 125 miles.

Step-by-step explanation:

Speed of Gary = 50 miles/hour

Time taken by Gary to reach the park from his house = 2.5 hours

Now, we know that,

Distance travelled = speed × time

So,  distance between park and Gary's house = speed × time

= 50 × 2.5

= 125 miles

So, the park is 125 miles away from the Gary's house.

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A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the
hichkok12 [17]

Answer:

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

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}}

A statistician calculates that 8% of Americans own a Rolls Royce.

This means that p = 0.08

Sample of 595:

This means that n = 595

Mean and standard deviation:

\mu = p = 0.08

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111

What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05. So

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

By the Central Limit Theorem

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

Z = \frac{0.05 - 0.08}{0.0111}

Z = -2.7

Z = -2.7 has a p-value of 0.0035

2*0.0035 = 0.0070

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

8 0
3 years ago
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