The probability that a randomly selected 2-year-old male salamander will live to
ID: 3366735 • Letter: T
Question
The probability that a randomly selected 2-year-old male salamander will live to be 3 years old is 0.97865 (a) What is the probability that two randomly selected 2-year-old male salamanders will live to be 3 years old? (b) What is the probability that seven randomly selected 2-year-old male salamanders will live to be 3 years old? (c) What is the probability that at least one of seven randomly selected 2-year-old male salamanders will not live to be 3 years old? Would it be unusual if at least one of seven randomly selected 2-year-old male salamanders did not live to be 3 years old? (a) The probability that two randomly selected 2-year-old male salamanders will ive to be 3 years old is Round to five decimal places as needed.)Explanation / Answer
Solution :
Given that P(2?-year-old male salamander will live to be 3 years? old) = 0.97865
(a) probability of all 'n' salamanders living to age 3 years = (0.97865)^n
=> The probability that 2 randomly selected 2?-year-old male salamanders will live to be 3 years? old is (0.97865)^2 = 0.95776
(b) => The probability that 7 randomly selected 2?-year-old male salamanders will live to be 3 years? old is (0.97865)^7 = 0.85979
(c) Given that n = 7 , p = 1 - 0.97865 = 0.02135 (probability that a 2?-year-old male salamanders will not live to be 3 years? old)
=> P(x >= 1) = 0.14021
Formula : for binomial nCr*p^r*(1 - p)^(n - r)
=> At 5 % significance level, this is not unusual since 0.14 > 0.05
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