This problem uses the empirical rule (68-97-99.7) and the alternate empirical ru

Question

This problem uses the empirical rule (68-97-99.7) and the alternate empirical rule (steps of 1/3 sigma) to obtain the answers.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.962 g and a standard deviation of 0.329 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine.

In what range would you expect to find the middle 95% of amounts of nicotine in these cigarettes (assuming the mean has not changed)?
Between--- and ---.

If you were to draw samples of size 57 from this population, in what range would you expect to find the middle 95% of most average amounts of nicotine in the cigarettes in the sample?
Between --- and ---

Explanation / Answer

For the normal distribution, the values within onestandard deviation of the mean account for 68.27% of the set; while within two standard deviations account for 95.45%; and within three standard deviations account for 99.73%.

a) 95% is two SDs away.

Range = {0.962 - 2 * 0.329, 0.962 + 2 * 0.329}

Range = {0.304, 1.62}

b) t lies between -2 and 2

-2 = (x - 0.962)/0.329

x = 0.304

Also,

2 = (x - 0.962)/0.329

x = 1.62

Range = {0.304, 1.62}

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