How do you Estimate the Product of Decimals and Whole

Mathematics

1 answer:

PtichkaEL [24]3 years ago

8 0

Answer:

1) 8.5

2) 60

3) 69.3

4) 6.8

5) 3.6

6) 10.5

Step-by-step explanation:

Take out the decimal of the estimated factors and multiply. Count how far to left the decimal is in the factors. In the product, put the decimal as many to the left as it was in the factors. (ex. 6.93 x 42, 6.93 rounds to 6.9, 42 rounds to 40, 69 x 40 = 2,760, move the decimal over one for correct place value, 6.9 x 40 = 276.0 or 276)

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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.

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