Question 1085659: The probability of tossing heads with a weighted coin is 0.4. If this unfair coin is tossed
50 times, what is the probability that heads will appear between 15 and 25 times,
inclusive? (Use the normal approximation, if valid.)
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
First we see whether the normal approximation is valid by
calculating np and n(1-p) to see whether they are both at
least 5. np = (50)(0.4) = 20 and n(1-p) = (50)(1-0.4) =
(50)(0.6) = 30. So the approximation is valid.
The word "inclusive" follows the words "between 15 and
25 times". Therefore, we get the area under the normal curve
from 0.5 less than the smaller value 15, that is, from x=14.5
to 0.5 greater than the greater value 25, that is, to x=25.5.
We can do this either with technology or with a normal table.
With a TI-84
normalcdf(14.5,25.5,50*0.4,√(50*.4*0.6))
We get 0.8876487995
[Personally, I doubt that is any more accurate than 0.8 or 0.9]
Edwin
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