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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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A sample of 64 observations has been selected to test whether the population mean is smaller than 15. The sample showed an avera
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H0 : μ ≥ 15

H1 : μ < 15

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Duke pays $111.60 for his yearly movie pass plus $4.00 for popcorn for each movie.Tenneshia pays $16.40 for a ticket to every mo
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Answer:

After 9 movies they will have paid the same amount

Step-by-step explanation:

We must write an equation for Duke's expenses and an equation to represent Tennessee's expenses.

<u>For Duke expenses we have:</u>

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The equation that represents the expenses is a linear equation like the one shown below

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A variable expense of $ 16.40 for each film.

The equation that represents the expenses is a linear equation like the one shown below

C = 16.40x

Where C represents the cost and x the number of movies.

To know after how many movies have paid the same amount, we equate both equations and solve the variable x

111.60 +4.00x=16.40x\\\\16.40x - 4x = 111.60\\\\12.40x =111.60\\\\x =\frac{111.60}{12.40}\\\\x =9

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