Miss Jane shoots at a target with a round bull's-eye of radius 1.4 centered at 0. The horizontal and vertical distances from the center at which she shoots are independent random Normal variables with mean 0 and variance 3. She shoots until she hits the bull's--eye. a) What is the probability that Miss Jane won't hit the bull's-eye with one shot? b) What is the probability that Miss Jane will hit the bull's-eye at the 4-th shot? c) To make the game more difficult, the bull's-eye is considered hit only if Miss Jane will hit between 0.7 and 1.4 from the center. What is the probability she will hit the bull's-eye at the 4-th shot?
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!
Miss Jane shoots at a target with a round bull's-eye of radius 1.4 centered at 0. The horizontal and vertical distances from the center at which she shoots are independent random Normal variables with mean 0 and variance 3. She shoots until she hits the bull's--eye.
a) What is the probability that Miss Jane won't hit the bull's-eye with one shot?
b) What is the probability that Miss Jane will hit the bull's-eye at the 4-th shot?
c) To make the game more difficult, the bull's-eye is considered hit only if Miss Jane will hit between 0.7 and 1.4 from the center. What is the probability she will hit the bull's-eye at the 4-th shot?
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