In a game, a ball is thrown and lands in one of 4 slots, labelled $$\(A, B, C\)$$ and $$\(D\)$$. Raju wishes to test whether the probability that the ball will land in slot $$\(A\)$$ is $$\(\frac{1}{4}\)$$. The ball is thrown 100 times and it lands in slot $$\(A 15\)$$ times. Use a suitable approximating distribution to carry out the test at the $$\(2 \%\)$$ significance level. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_62 Year：2021 Question No：1(b)
Answer:
\(\mathrm{N}\left(25, \frac{75}{4}\right)\)
\(\pm \frac{15.5-25}{\sqrt{\frac{75}{4}}}\) or \(\frac{\frac{15.5}{100}-0.25}{\sqrt{\frac{0.25 \times 0.75}{100}}}\)
\(\pm-2.194(2.19)\)
\(-2.326<-2.194\) or \(0.0141>0.01\) or \(0.9859<0.99\)
No evidence to reject that the probability is \(\frac{1}{4}\)
\(\pm \frac{15.5-25}{\sqrt{\frac{75}{4}}}\) or \(\frac{\frac{15.5}{100}-0.25}{\sqrt{\frac{0.25 \times 0.75}{100}}}\)
\(\pm-2.194(2.19)\)
\(-2.326<-2.194\) or \(0.0141>0.01\) or \(0.9859<0.99\)
No evidence to reject that the probability is \(\frac{1}{4}\)
Knowledge points:
6.5.2.2 a normal approximation to the binomial or the Poisson distribution, where appropriate
Solution:
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