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Sladkaya [172]
3 years ago
10

(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the

nearest whole number.)
Mathematics
1 answer:
goblinko [34]3 years ago
8 0
Given that the scale readings of the laboratory scale is normally distributed with an unknown mean and a standard deviation of 0.0002 grams.

Part A:

If the weight is weighted 5 times and the mean weight is 10.0023 grams, the 98% confidence interval for μ, the true mean of the scale readings is given by:

98\% \ C. \ I.=\bar{x}\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) \\  \\ =10.0023\pm2.33\left(\frac{0.0002}{\sqrt{5}}\right) \\  \\ =10.0023\pm2.33(0.000089) \\  \\ =10.0023\pm0.00021 \\  \\ =(10.0023-0.00021, \ 10.0023+0.00021) \\  \\ =(10.0021, \ 10.0025)

Thus, we are 98% confidence that the true mean of the scale readings is between 10.0021 and 10.0025.



Part B:

To get a margin of error of +/- 0.0001 with a 98% confidence, then

\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)=\pm0.0001 \\ \\ \Rightarrow2.33\left(\frac{0.0002}{\sqrt{n}}\right)=0.0001 \\  \\ \Rightarrow\left(\frac{0.0002}{\sqrt{n}}\right)= \frac{0.0001}{2.33} =0.0000429 \\  \\ \Rightarrow\sqrt{n}= \frac{0.0002}{0.0000429} =4.66 \\  \\ \Rightarrow n=4.66^2=21.7156\approx22

Therefore, the number of <span>measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence is 22.</span>
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Fernando cleans pools for the summer for $25 an hour plus a supply fee of $15.
puteri [66]

Answer:

15x+25 ; 70

Step-by-step explanation:

Given that,

Fernando cleans pools for the summer for $25 an hour plus a supply fee of $15.

Here, $25 is constant and $15 increases as the number of hour increase. For x hours, the cost for Fernando to clean a pool is given by :

y = 15x+25

For 3 hours,

y = 15(3)+25

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So, the required option is (c) " 15x+25 ; 70 ".

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Step-by-step explanation:

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Tcecarenko [31]

Answer:

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Step-by-step explanation:

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6 0
2 years ago
Find a linear equation to model this real-world application:
SSSSS [86.1K]

The linear equation to model the company's monthly expenses is y = 2.5x + 3650

<em><u>Solution:</u></em>

Let "x" be the units produced in a month

It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers.

Cost per unit = $ 2.50

The company has monthly operating expenses of $350 for utilities and $3300 for salaries

We have to write the linear equation

The linear equation to model the company's monthly expenses in the form of:

y = mx + b

Cost per unit = $ 2.50

Monthly Expenses = $ 350 for utilities and $ 3300 for salaries

Let "y" be the total monthly expenses per month

Then,

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Thus the linear equation to model the company's monthly expenses is y = 2.5x + 3650

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Find the degree of the polynomial: 5ab^3−7a^5c^2−5
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Step-by-step explanation:


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