For each of the situations below, define a random variable. Decide if it follows a binomial or Poisson distribution (or neither) and indicate the relevant numerical values. For the binomial, this is the number of trials (n) and the probability of success (p). For Poisson, this is the average over the interval (). Write the question asked with probability symbols. Do not compute the probability.   A technician is responsible for a large number of machines at a laboratory. On average, machines need minor adjustments 8 times every hour. The technician will be on a break for 30 minutes. What is the probability that no machines need adjusting while he is on break? According to the  CDC (Links to an external site.), about 10% of Washington state adults suffer from asthma. Suppose I select a sample of 13 random adults. What is the probability that more than 5 of them have asthma.

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Q: continuous random variables?

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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!