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2 years ago

B. What number is equal to 280 tenths + 19 thousandths? HELP!!

Mathematics

1 answer:

Kaylis [27]2 years ago

3 0

The number that equals 280 tenths + 19 thousandths is 28.019

<h3>How to determine the number?</h3>

The statement is given as:

280 tenths + 19 thousandths

Rewrite the terms of the expression as fractions

So, we have

280/10 + 19/1000

Evaluate the quotients

28.0 + 0.019

Add both numbers

28.019

Hence, the number that equals 280 tenths + 19 thousandths is 28.019

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2 years ago

Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58, what is the

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Answer:

0.36% probability that fewer than half in your sample will watch news videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 250, p = 0.58$

$\mu = E(X) = 250*0.58 = 145$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80$

If the population proportion of adults who watch news videos is 0.58, what is the probability that fewer than half in your sample will watch news videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

$Z = \frac{124 - 145}{7.8}$