-Cans of regular coke are supposed to contain 12 oz. of cola. If a quality contr

Question

-Cans of regular coke are supposed to contain 12 oz. of cola. If a quality control engineer finds that the production process results in cans of Coke having a mean of 12 oz., can she conclude that the production process is processing as it should? Why or why not?

-Helen Mirren won an Oscar for best actress at 61 years of age. The Oscar-winning best actresses have a mean age of 35.8 years and a standard deviation of 11.3 years.

a) Convert Helen Mirren's age to a z score.

b) If we consider "usual" ages to be those that convert to z scores between -2 and 2 (empirical rule--95% of people fall within 2 standard deviations of the mean), is Helen Mirren's age usual or unusual? Why?

Explanation / Answer

a)

Yes, surely, at any significance level, because the sample readily proves that the mean is 12 oz. Besides, he will get a t statistic of 0, which will always have a P-value of 1 (for two tailed) and 0.50 for 1 tailed, which is large.

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a)

z = (x - u) / sigma = (61-35.8)/11.3 = 2.230088496 [answer]

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b)

The usual ages are

u - 2s < x < u + 2s

35.8 - 2*11.3 < x < 35.8 + 2*11.3

13.2 < x < 58.4

in which 61 is out of this interval. HENCE, HER AGE IS UNUSUAL. [ANSWER]

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