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1 year ago

Mr. Haley is leaning a ladder against the side of his house to repair the roof.

Mathematics

1 answer:

natima [27]1 year ago

5 0

Answer:

15 ft

Explanation:

We can represent the situation with the following figure

Therefore, the length of the ladder is the hypotenuse of the right triangle formed, where the legs are 12 ft and 9 ft. Using the Pythagorean theorem, we can calculate the length of the ladder as

$\begin{gathered} Ladder=\sqrt{12^2+9^2} \\ Ladder=\sqrt{144+81} \\ Ladder=\sqrt{225} \\ Ladder=15 \end{gathered}$

Therefore, the length of the ladder is 15 ft

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Step-by-step explanation:

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substitute

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Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

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.

We have:

Mean $\mu$ , standard deviation $\sigma$ .

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

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

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