There is about 80% chance that a randomly selected person aged 20 will still be
ID: 3201044 • Letter: T
Question
There is about 80% chance that a randomly selected person aged 20 will still be alive at age 65, according to the U.S. National Center for Health Statistics. Suppose that you randomly select forty 20-year-olds. What is the probability that at least 35 of the 40 persons are still alive at age 65? Math formula: (Write the mathematical formula, with standard notation, for the probability.) Excel commands: Numerical answer: What is the probability that between 10 and 25 (both inclusive) persons are alive at age 65? Math formula: (Write the mathematical formula, with standard notation, for the probability.) Excel commands: Numerical answer:Explanation / Answer
Probability that a person aged 20 years will be alive at 65 years of age: P (A) = .80
Probability that a person aged 20 years will not be alive at 65 years of age: P(NA) = .20
a) Probability of atleast 35 people out of 40 will be alive at 65 years of age
Maths Formula : P(1A2A3A......35A1D2D3D4D5D) + P(1A2A3A......36A1D2D3D4D) + P(1A2A3A......37A1D2D3D) + P(1A2A3A......38A1D2D) + P(1A2A3A......39A1D) + P(1A2A3A......40A)
Excel Command: [POWER(.80,.35) * POWER (.20,5)] + [POWER(.80,.36) * POWER (.20,4)] + [POWER(.80,.37) * POWER (.20,3)] + [POWER(.80,.38) * POWER (.20,2)] + [POWER(.80,.39) * POWER (.20,1)] + POWER(.80,.40)
Numerical answer = .000177
b) Probability of between 10 and 25 people out of 40 will be alive at 65 years of age
Maths Formula = P(1A2A3A......10A1D2D3D......30D) + P(1A2A3A......11A1D2D3.......29D) +....... + P(1A2A3A...25A1D2D........15D)
Excel Command = [POWER(.80,.10) * POWER (.20,30)] + [POWER(.80,.11) * POWER (.20,29)] + [POWER(.80,.12) * POWER (.20,28)]..........................................................[POWER(.80,.25) * POWER (.20,15)].
Numberical Answer = 1.65059E-13
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