Mehmet wants to meet his childhood love Alev. He has not seen her since they were both ten years old and he wants to impress her by giving a ring to her as a gift. Alev would appreciate (be impressed by) Mehmet if the ring fits her "ring finger". Mehmet doesn't know anything about her finger so he randomly selects a ring from a shop. The diameters of the rings at the shop follows the normal distribution with a mean value of 1.0+(3/10) cm and a standard deviation of 0.4 cm. The diameters of the fingers of 28-year-old-women (Alev's age is 28) in town also have a normal distribution with a mean value of 1.0+(2/10) cm and a standard deviation of 0.8 cm. A ring fits a finger if the diameter of the ring is greater than the diameter of the finger and the difference between these diameters is not greater than 0.2 centimeter. What is the probability that Mehmet will impress her?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Mehmet wants to meet his childhood love Alev. He has not seen her since they were both ten years old and he wants to impress her by giving a ring to her as a gift. Alev would appreciate (be impressed by) Mehmet if the ring fits her "ring finger". Mehmet doesn't know anything about her finger so he randomly selects a ring from a shop. The diameters of the rings at the shop follows the
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