Question: Given a random variable X, which can follow different probability distributions such as Normal, Binomial, or Poisson. The mean () and standard deviation ( ()

Given a random variable X, which can follow different probability distributions

Given a random variable X, which can follow different probability distributions such as Normal, Binomial, or Poisson. The mean () and standard deviation ( () of X are known. Question: If X follows a Normal Distribution with a mean of 50 and a standard deviation of 10, what is the probability that X will take a value less than 45 ? Additionally, if X follows a Binomial Distribution with parameters n (number of trials) and p (probability of success on each trial), and you know that the mean is 5 and the standard deviation is 2, can you determine the values of n and p ? Finally, if X follows a Poisson Distribution with a known mean of 10 , what is the probability that X will take a value of 15

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