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4 years ago

HELP PLEASE!!! Need help with 11 or 12 Thank you!!!

Mathematics

1 answer:

qwelly [4]4 years ago

6 0

Answer:

11) 30.7

12) 16.3

Step-by-step explanation:

11)

$\dfrac{\sin 50}{12}=\dfrac{\sin B}{8}$

Multiply both sides by 8:

$\sin B=\dfrac{2\sin 50}{3}$

$B=\sin^{-1}\dfrac{2\sin 50}{3}\approx 30.7$

12)

$\dfrac{\sin 25}{7}=\dfrac{\sin 80}{C}$

$C=\dfrac{\sin 80}{\frac{\sin 25}{7}}\approx 16.3$

Hope this helps!

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4 years ago

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Answer:

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$E(\bar X) = \mu$

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(100,15)$

Where $\mu=100$ and $\sigma=15$

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Because by definition:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$E(\bar X) = \mu$

$Var(\bar X) = \frac{\sigma^2}{n}$

And for this case we have this:

$\mu_{\bar X}= \mu = 100$

$\sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75$

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