How are taxi fares calculated?

The fares received by taxi drivers working for the City Taxi line is normally distributed with a mean equal to?

• The fares received by taxi drivers working for the City Taxi line is normally distributed with a mean equal to $12.50 and a standard deviation equal to $3.25. Based on this information, what is the probability that a specific fare will exceed $15.00 Suppose the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes, then what is the probability that it will take exactly 5 minutes The fares received by taxi drivers working for the City Taxi line is normally distributed with a mean equal to

• Answer:

  1. Use z-score chart to find probability: http://www.regentsprep.org/Regents/math/algtrig/ATS7/ZChart.htm P(x > 15) = P(Z > (15−12.5)/3.25) = P(Z > 0.77) = 1 − P(Z < 0.77) = 1 − 0.7794 = 0.2206 ------------------------------ 2. Probability density function: f(x) = c where c = 1/(8−3) = 1/5 f(x) = 1/5 for 3 ≤ x ≤ 8 Cumulative distribution function: F(x) = ∫₃ˣ f(x) dx for 3 ≤ x ≤ 8 F(x) = ∫₃ˣ 1/5 dx = 1/5 C |₃ˣ = (x−3)/5 F(x) = (x−3)/5 Now uniform distribution is a continuous distribution, so it is not possible to find probability of X at a single number. Just like in normal distribution, we can find probability that X is within a certain range: P(X < 5) = F(5) = (5−3)/5 = 2/5 P(X > 5) = 1 − F(5) = 1 − 2/5 = 3/5 P(3.5 < X < 5) = F(5) − F(3.5) = (5−3)/5 − (3.5−3)/5 = 2/5 − 1/10 = 3/10 etc...