peytondavis2424
31.07.2019 •
Mathematics
If the probability of hearing a "yes" to a campaign contribution drive is 0.07, and 250 requests are made, what is the probability of getting at least 20 positive responses?
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Ответ:
The number of successes, x, is then given bywhere
=0.30069 to 5 decimal places using binomial distribution
Note: it is possible to actually do the summation (as is done here), or refer to binomial tables/software, or to use the normal approximation, with continuity correction, as shown below.
mean number of responses = np = 250*0.07 = 17.5
variance of responses = npq = np(1-p) = 250(0.07)(0.93)=16.275
standard deviation = sqrt(16.275)=4.0342
P(X>=19.5)
=1-P(X<19.5)
=1-P(Z<(X- μ )/ σ )
=1-P(Z< (19.5-17.5)/4.0342)
=1-P(Z<0.49576)
=1-0.689967
=0.3100 (using normal approximation)
Ответ: