In a state with 100 dams, the probability that a dam is dry is 0.7. For a year, the state government declares a drought if at least 75 dams are dry, while the central government declares a drought if at least 80 dams are dry. Using normal approximation, find the probability that for a year, the decision of the state government to declare a drought is not approved by the central government. [4] [CO01]
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!
![In a state with 100 dams, the probability that a dam is dry is 0.7. For a year, the state
government declares a drought if at least 75 dams are dry, while the central government
declares a drought if at least 80 dams are dry. Using normal approximation, find the
probability that for a year, the decision of the state government to declare a drought is not
approved by the central government.
[4] [CO01]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8828776-f116-4f63-8356-50b1e1afaa3a%2F56f5122d-a989-471f-b80d-a37070b2a81a%2F3ucgcj_processed.png&w=3840&q=75)
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