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P(t)=(0.82)^(t)
A local department of transportation has determined that on a particular bus route, the probability of waiting more than 
t minutes for a bus at a certain intersection is modeled by the function shown. What is the best description of the meaning of 0.82 in this context?
Choose 1 answer:
(A) The probability that a person will have to wait more than 1 minute for a bus is 
82%.
(B) 
82% of the buses are on the bus route at any given time.
(C) 
82% of the buses on the route are late.
(D) The probability that a person will have to wait less than 1 minute for a bus is 
82%.

P(t)=(0.82)t P(t)=(0.82)^{t} \newlineA local department of transportation has determined that on a particular bus route, the probability of waiting more than t t minutes for a bus at a certain intersection is modeled by the function shown. What is the best description of the meaning of 00.8282 in this context?\newlineChoose 11 answer:\newline(A) The probability that a person will have to wait more than 11 minute for a bus is 82% 82 \% .\newline(B) 82% 82 \% of the buses are on the bus route at any given time.\newline(C) 82% 82 \% of the buses on the route are late.\newline(D) The probability that a person will have to wait less than 11 minute for a bus is 82% 82 \% .

Full solution

Q. P(t)=(0.82)t P(t)=(0.82)^{t} \newlineA local department of transportation has determined that on a particular bus route, the probability of waiting more than t t minutes for a bus at a certain intersection is modeled by the function shown. What is the best description of the meaning of 00.8282 in this context?\newlineChoose 11 answer:\newline(A) The probability that a person will have to wait more than 11 minute for a bus is 82% 82 \% .\newline(B) 82% 82 \% of the buses are on the bus route at any given time.\newline(C) 82% 82 \% of the buses on the route are late.\newline(D) The probability that a person will have to wait less than 11 minute for a bus is 82% 82 \% .
  1. Calculate Probability for t=1t=1: The function P(t)=(0.82)tP(t)=(0.82)^t gives the probability of waiting more than tt minutes for a bus. To understand what 0.820.82 means, we look at the case when t=1t=1.
  2. Interpret Probability Value: Calculate P(1)P(1) to see the probability of waiting more than 11 minute. P(1)=(0.82)1=0.82P(1)=(0.82)^{1} = 0.82, which means there's an 82%82\% chance of waiting more than 11 minute.
  3. Describe 0.820.82 Probability: Since P(1)P(1) is 0.820.82, the best description of 0.820.82 is the probability that a person will have to wait more than 11 minute for a bus.

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