The amounts of nicotine in a certain brand of cigarette are normally distributed

Question

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.951 g and a standard deviation of 0.328 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 98% of amounts of nicotine in these cigarettes (assuming the mean has not changed)? Between_ and _

If you were to draw samples of size 30 from this population, in what range would you expect to find the middle 98% of most average amounts of nicotine in the cigarettes in the sample? Between _ and _

Both answers should be accurate to 4 decimal places!

Explanation / Answer

a) Middle 98%

Lower value = -2.32635*0.328+0.951 = 0.1880

Upper value = 2.32635*0.328+0.951 = 1.7140

So, range is (0.1880, 1.7140)

b) Lower value = -2.32635*(0.328/Sqrt(30))+0.951 = 0.8117

Upper value = 2.32635*(0.328/Sqrt(30))+0.951 = 1.0903

So, range is (0.8117, 1.0903)

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