Respuesta :
Answer:
P(X=13) = 0.0758
Step-by-step explanation:
Binomial Distribution Condition:
- There is only 2 outcomes → either arrive on time or not on time.
- There is a fixed number of trials → 13 flights.
- Each trial is independent of all other trials → assuming each flight does not affect others on their arrival time.
- The probability of success is constant → assuming success rate of 82% is constant for each trial.
Binomial Distribution Formula:
[tex]\boxed{P(X=x)=_nC_x\cdot p^x\cdot q^{n-x}}[/tex]
where:
- P(X=x) = the probability of event X which has x successes
- n = number of trial
- x = number of successes
- p = success rate
- q = fail rate
Given:
- X = event of flight arrives on time
- n = 13
- x = 13
- p = 82% = 0.82
- q = 1 - p = 1 - 0.82 = 0.18
[tex]P(X=13)=_{13}C_{13}(0.82)^{13}(0.18)^{13-13}[/tex]
[tex]\displaystyle=\frac{13!}{13!0!} (0.82)^{13}(0.18)^0[/tex]
[tex]=1\times(0.82)^{13}\times1[/tex]
[tex]=0.0758[/tex]
