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12 April, 04:52

The ski lift at Thunder Mountain called Devils Canyon is quite dangerous. Usually 2% of the skiers who attempt the run will injure themselves due to falls.

8. What is the probability that exactly 3 of the next 100 skiers who attempt this run will injure themselves?

Answer Choices:

0.126

0.175

0.182

0.215

+2
Answers (1)
  1. 12 April, 08:17
    0
    This problem involves a Bernoulli trial with the binomial distribution.

    p = 2% = 0.02, the probability of injury

    q = 1 - p = 0.98, the probability of no injury.

    n = 100, the number of trials (skiers)

    r = 3, expected number of injuries

    The probability of 3 injuries is

    P (3 of 100) = ₁₀₀C₃ p³q (¹⁰⁰⁻³)

    = 161700 * (0.02³) * (0.98⁹⁷)

    = 0.1823

    Answer: 0.182
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