Construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in nonfiltered and filtered cigarettes. Do the cigarette filters appear to be effective? (Hint: The filters reduce the amount of tar ingested by the smoker.) Tar (mg) in Nonfiltered Cigarettes Frequency Tar (mg) in Filtered Cigarettes Frequency 19−24 1 7−12 3 25−30 0 13−18 3 31−36 15 19−24 6 37−42 7 25−30 13 43−48 2 Click the icon to view the frequency distributions. Complete the relative frequency table below. Tar (mg) Relative Frequency (Nonfiltered) Relative Frequency (Filtered) 7−12 nothing% nothing% 13−18 nothing% nothing% 19−24 nothing% nothing% 25−30 nothing% nothing% 31−36 nothing% nothing% 37−42 nothing% nothing% 43−48 nothing% nothing% (Simplify your answers.) Do cigarette filters appear to be effective? A. No, because the relative frequencies for each are not substantially different. B. No, because the relative frequency of the higher tar classes is greater for filtered cigarettes. C. Yes, because the relative frequency of the higher tar classes is greater for nonfiltered cigarettes. D. This cannot be determined.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Tar (mg) in
Nonfiltered
Cigarettes
|
Frequency
|
|
Tar (mg) in
Filtered
Cigarettes
|
Frequency
|
|
---|---|---|---|---|---|
19−24
|
1
|
7−12
|
3
|
||
25−30
|
0
|
13−18
|
3
|
||
31−36
|
15
|
19−24
|
6
|
||
37−42
|
7
|
25−30
|
13
|
||
43−48
|
2
|
|
Tar (mg)
|
Relative
Frequency
(Nonfiltered)
|
Relative
Frequency
(Filtered)
|
---|---|---|
7−12
|
nothing%
|
nothing%
|
13−18
|
nothing%
|
nothing%
|
19−24
|
nothing%
|
nothing%
|
25−30
|
nothing%
|
nothing%
|
31−36
|
nothing%
|
nothing%
|
37−42
|
nothing%
|
nothing%
|
43−48
|
nothing%
|
nothing%
|
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