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Answer:
So we expect about 50% of the middle values within 0.705 and 1.103 g
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the amounts of nicotine in a certain brand of a population, and for this case we know the distribution for X is given by:
Where and
And the best way to solve this problem is using the normal standard distribution and the z score given by:
We want to find a two values that accumulates the middel 50% of the data. So we need to find a quantile who accumulates (1-0.5)/2 = 0.25 of the area on each tail and we got:
Since P(Z<-0.674) = 0.25 and P(Z>0.674) =0.25. And using this value we can find the possible values of X
So we expect about 50% of the middle values within 0.705 and 1.103 g