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A poll is given, showing 35% are opposed to a city hall renovation project.
If 8 people are chosen at random, what is the probability that exactly 6 of them oppose the city hall
renovation project?
Round your answer to 4 places after the decimal point, if necessary.

Respuesta :

The probability that exactly 6 of them will oppose the renovation project is 0.0217

Data

  • Number of them opposing the hall = 6
  • Sample size = 8
  • P = 35% = 0.35

Probability of Exactly 6 opposing the Hall

The probability that exactly 6 of them oppose the city hall renovation project can be calculated as

[tex]P(X=x)=^nC_x*P^x(1-P)^n^-^x\\P(X=6)=^8C_6*0.35^6*(1-0.35)^8^-^6\\P(X=6)=^8C_6*0.35^6*0.65^2\\P(X=6)=28*0.00184*0.4225\\P(X=6)=0.0217[/tex]

The probability that exactly 6 of them will oppose the renovation project is 0.0217

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