TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/4.2
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- Coin throws
An unfair coin is thrown 600 times. The probability of geting a tail in each throw is 1/4.
- (a) Use a Binomial distribution to compute the probability that the number of heads obtained does not differ more than 10 from 250.
- (b) Use a Normal approximation without a continuity correction to calculate the probability in (a). How does the result change if the approimation is provided with a continuity correction?
Lösungsvorschlag von Gittenburg[Bearbeiten | Quelltext bearbeiten]
--Gittenburg 07:17, 4. Nov. 2019 (CET)
(a)
> pbinom(250+10, 600, 3/4) - pbinom(250-10, 600, 3/4) [1] 5.675012e-61
Eventuell ist das ein Tippfehler in der Angabe und 450 ist gemeint:
> pbinom(450+10, 600, 3/4) - pbinom(450-10, 600, 3/4) [1] 0.6540917
Lösungsvorschlag von Jeremyer[Bearbeiten | Quelltext bearbeiten]
--Jeremyer 07:17, 9. Nov. 2020(CET)
(b)
> n = 600 > p = 3/4 > q = 1 - p > a = 450 - 10 > b = 450 + 10
Without continuity correction
> pnorm((b - (n*p))/sqrt(n*p*q)) - pnorm((a - (n*p))/sqrt(n*p*q)) [1] 0.6542214
With continuity correction
> pnorm((b + 0.5 - (n*p))/sqrt(n*p*q)) - pnorm((a - 0.5 - (n*p))/sqrt(n*p*q)) [1] 0.6778012