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3 years ago

Write 12.5% as a fraction or mixed number in simplest form

Mathematics

2 answers:

olga2289 [7]3 years ago

6 0

12.5% in decimal form is 0.125

1/8 = 0.125

Your answer = 1/8

lianna [129]3 years ago

6 0

Answer: 1/8

Step-by-step explanation: A percent is a ratio that compares a number to 100. So we can write 12.5% as 12.5/100.

Next, we need to get rid of the decimal. We can multiply the numerator and denominator of a fraction by the same number without changing the value of the fraction.

So to get rid of the decimal, we can multiply the numerator and the denominator of 12.5/100 by 10 and we have 125/1000.

Now, notice that 125/1000 is not in lowest terms because we can divide the numerator and the denominator by 125 to get 1/8.

So 12.5% can be written as the fraction 1/8.

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3 years ago

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2 years ago

A researcher believes that 9% of females smoke cigarettes. If the researcher is correct, what is the probability that the propor

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Answer:

The probability that the sample proportion would differ from the population proportion by more than 3% is 0.0027.

Step-by-step explanation:

Let X = number of females who smoke cigarettes.

The probability that a female smoke cigarettes is, p = 0.09.

A random sample of size, n = 703 females were selected to determine the sample proportion of females who smoke cigarettes.

A female smoking cigarettes is independent from others.

The random variable X follows a Binomial distribution with parameters n = 703 and p = 0.09.

Now, as the sample size is quite large, i.e. n = 703 > 30, according to the Central limit theorem the sampling distribution of sample proportion can be described by the Normal distribution.

The mean of this sampling distribution is same as the population proportion, i.e. $\mu_{\hat p}=p=0.09$ .

And the standard deviation of the sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.09(1-0.09)}{703}}=0.0108$

Compute the probability that the sample proportion would differ from the population proportion by more than 3% as follows:

$\hat p-p>0.03\\\hat p>0.03+p\\\hat p>0.03+0.09\\\hat p>0.12$

Compute the value of $P(\hat p>0.12)$ as follows:

$P(\hat p>0.12)=P(\frac{\hat p-p}{\sigma_{\hat p}}>\frac{0.03}{0.0108})\\=P(Z>2.78)\\=1-P(Z$

Thus, the probability that the sample proportion would differ from the population proportion by more than 3% is 0.0027.

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3 years ago