4 years ago

PLEASE HELP

Mathematics

1 answer:

Sliva [168]4 years ago

5 0

Which is the amount of students wearing blue shirts 28 or 36?

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The lengths of text messages are normally distributed with a population standard deviation of 4 characters and an unknown popula

umka21 [38]

Answer:

The answer is " $(25.32, 30.68)$ "

Step-by-step explanation:

Given:

$\bar x = 28\\\\ \sigma = 4\\\\n =26\\\\$

When $98\%$ confidence level so, the z:

$\alpha = 1 - 98\% = 1 - 0.98 = 0.2\\\\\frac{\alpha}{2} =\frac{0.02}{2} = 0.01\\\\Z_{\frac{\alpha}{2}} = Z_{0.01} = 1.645\ \ \ ( Using \ z \ table )\\\\$

$E = Z_{\frac{\alpha}{2} \times ( \frac{\sigma}{\sqrt{n}})$

$= 1.645 \times (\frac{4}{\sqrt{26}})\\\\=2.68$

When 98% confidence interval estimate of the population mean is,

$\bar x - E < \mu < \bar x + E\\\\28 - 2.68 < \mu < 28 + 2.68\\\\25.32 < \mu < 30.68\\\\(25.32, 30.68)\\\\$

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3 years ago