How much sugar do reduced sugar cookies typically have? You take a random sample of 51 reduced-sugar cookies and test them in a lab, finding a mean sugar content of 3.2 grams and a standard deviation of 1.1 grams of sugar. Create a 99% confidence interval for the mean grams of sugar.

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Answer:  [tex](2.8,\ 3.6)[/tex]

Step-by-step explanation:

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

Given : Sample size : n= 51   ( >30 , that means its a large sample)

Sample mean : [tex]\overlien{x}=3.2\text{ grams}[/tex]

Standard deviation : [tex]\sigma=1.1\text{ grams}[/tex]

Significance level : [tex]1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=\pm2.576[/tex]

Now, the 99% confidence interval for the mean grams of sugar will be :-

[tex]=3.2\pm(2.576)\times\dfrac{1.1}{\sqrt{51}}\\\\\approx3.2\pm0.40\\\\=(2.8,\ 3.6)[/tex]

Hence, the 99% confidence interval for the mean grams of sugar [tex]\mu[/tex] = [tex](2.8,\ 3.6)[/tex]

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