SUMMARIZING POSSIBLE OUTCOMES AND THEIR PROBABILITIESAll possible outcomes and probabilities are summarized in a probability distribution. There is a normal and a binomial distribution. A random variable is a numerical measurement of the outcome of a random phenomenon. The probability distribution of a discrete random variable assigns a probability to each possible value. Numerical summaries of the population are called parameters and a population distribution is a type of probability distribution, one that applies for selecting a subject at random from a population.The formula for the mean of a probability distribution for a discrete random variable is:μ= ΣxP(x)It is also called a weighted average, because some outcomes are likelier to occur than others, so a regular mean would be insufficient here. The mean of a probability distribution of random variable X is also called the expected value of X. The standard deviation of a probability distribution measures the variability from the mean. It describes how far values of the random variable fall, on the average, from the expected value of the distribution. A continuous variable is measured in a discrete manner, because of rounding. A probability distribution for a continuous random variable is used to approximate the probability distribution for the possible rounded values. PROBABILITIES FOR BELL-SHAPED DISTRIBUTIONSThe z-score for a value x of a random variable is the number of standard deviations that x falls from the mean. It is calculated as: The standard normal distribution is the normal distribution with mean and standard deviation . It is the distribution of normal z-scores.PROBABILITIES WHEN EACH OBSERVATION HAS TWO POSSIBLE OUTCOMESAn observation is binary if it has one of two possible outcomes (e.g: accept or decline, yes or no). A random variable X that counts the number of observations of a particular type has a probability distribution called the binomial distribution....