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3 years ago

NEED HELPPPP PLEASEEE!!! NUMBER 5 ONLY

Mathematics

1 answer:

Reika [66]3 years ago

7 0

Answer:

Let x equal the ice thickness. An equality that represents a safe ice thickness for walkability is:

x ≥ 4 inches

(Plus the graph)

Step-by-step explanation:

Defining a variable just means you let any letter or symbol take the place of something. But you have to specifically say what is what in order for it to be clear.

So I defined "x" as the variable to represent the ice's thickness. And since we want an inequality for all the safe thicknesses, we could say that "x" must be greater than or equal to 4 inches thick in order to safely walk on it.

Lastly, you'd graph it with a solid point on 4 with the arrow going to the right.

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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.

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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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

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