Find the missing side

Mathematics

1 answer:

Klio2033 [76]3 years ago

3 0

Answer:

28.3

Step-by-step explanation:

tan = opposite/adjacent

tan (58) = 1,600335

opposite = tan * adjacent

opposite = 1,600335 * 15 = 24,005018

For the Pytagorean theorem

x = √24,005018^2 + 15^2 = 28,306199 = 28.3

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Construct a confidence interval that will capture the true population mean with 95% confidence. Population standard deviation is

kompoz [17]

A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459 , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$

as population variance is unknown so we used sample variance

$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$

Now

$\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$$

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$