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Firdavs [7]
3 years ago
6

Work out the circumference of the circle of 6mm

Mathematics
1 answer:
Darina [25.2K]3 years ago
3 0
<h2>Answer :</h2>
  • Radius = 6 mm
  • Circumference = 2πr
  • = 2×6mm×π
  • =12π mm
  • = 12×3.14 mm
  • = 37.68 mm
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Answer:

a) The standard deviation of this sampling distribution is 2.07.

b) The missing number is 4.14.

c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

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.

In this question:

\mu = 272, n = 840, \sigma = 60

(a) If we take many samples, the sample mean x⎯⎯⎯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?

Using the Central Limit Theorem:

s = \frac{\sigma}{\sqrt{n}} = \frac{60}{\sqrt{840}} = 2.07

The standard deviation of this sampling distribution is 2.07.

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?

Within 2 standard deviations of the mean.

So, 2*2.07 = 4.14

The missing number is 4.14.

(c) What is the 95% confidence interval for the population mean score μ based on this one sample?

Within 4.14 of the mean

272 - 4.14 = 267.86

272 + 4.14 = 276.14

The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

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3 years ago
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Answer:

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Step-by-step explanation:

The fraction of all the cookies is equivalent to 1.


If \frac{1}{4} of the cookies are chocolate chip, then the remaining cookies is equivalent to

1-\frac{1}{4}=\frac{3}{4}.


The fraction of all the cookies that are peanut butter is


=\frac{1}{2}\times \frac{3}{4}


=\frac{3}{8}



8 0
2 years ago
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I think the answer is 6 or 9  Because the minimum is 3 I hope this helps.

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Answer:

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5|x³ - 2| + 7

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