germany-abitur 2025 Qa

germany-abitur · Other · abitur_nrw__typ_stochastik_lk 4 marks Binomial Distribution Compute Cumulative or Complement Binomial Probability
A total of 100 randomly selected bottles from this machine are to be examined. The random variable $X$: ``Number of underfilled bottles'' in a sample is assumed to be binomially distributed with $p = 0.3$.
(1) Determine the probability of the event ``Fewer than 30 underfilled bottles occur.''
(2) Give an event in the given context for which the probability can be calculated using the term $0.3 ^ { 4 } \cdot \binom { 96 } { 25 } \cdot 0.3 ^ { 25 } \cdot 0.7 ^ { 71 }$.
A total of 100 randomly selected bottles from this machine are to be examined. The random variable $X$: ``Number of underfilled bottles'' in a sample is assumed to be binomially distributed with $p = 0.3$.

(1) Determine the probability of the event ``Fewer than 30 underfilled bottles occur.''

(2) Give an event in the given context for which the probability can be calculated using the term $0.3 ^ { 4 } \cdot \binom { 96 } { 25 } \cdot 0.3 ^ { 25 } \cdot 0.7 ^ { 71 }$.
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