Cans of regular coke are supposed to contain 12 oz of cola I

-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?

Solution

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]