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kotykmax [81]
3 years ago
15

What is log base 7 of 252

Mathematics
1 answer:
rjkz [21]3 years ago
4 0

Answer:

2.84

Step-by-step explanation:

Recognize that 252 = 7*36

and so:

log base 7 of 252 = log base 7 of 36 + log base 7 of 7, or

                                 log base 7 of 36 + 1

So the most you can simplify log base 7 of 252 is to write 1 + log base 7 of 36.

Or, if you want to use the change of base formula, you could do the following:

                                 log 36

log base 7 of 36 = -------------- = 1.84

                                  log 7

and so log base 7 of 252 would come out to

1 + log base 7 of 36  =  1 + 1.84  = 2.84

Check:  does 7^2.84 = 252?  YES.  So we know that:

 1 + log base 7 of 36 = 2.84

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Answer:

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

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 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.

Mean $39725 and standard deviation $7320.

This means that \mu = 39725, \sigma = 7320

Sample of 125

This means that n = 125, s = \frac{7320}{\sqrt{125}}

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{39000 - 39725}{\frac{7320}{\sqrt{125}}}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

4 0
2 years ago
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