### Continuous probability distribution: A probability circulation in i m sorry the arbitrarily variable X can take on any type of value (is continuous). Due to the fact that there are infinite values the X could assume, the probability of X acquisition on any type of one particular value is zero. Because of this we often speak in ranges of values (p(X>0) = .50). The normal distribution is one instance of a constant distribution. The probability the X falls between two values (a and also b) amounts to the integral (area under the curve) native a come b:

The normal Probability Distribution

### We can convert any and also all normal distributions to the conventional normal circulation using the equation below. The z-score equates to an X minus the populace mean (μ) all split by the traditional deviation (σ).

Example typical Problem

### We want to determine the probability the a randomly selected blue crab has a weight higher than 1 kg. Based on previous study we assume that the distribution of weights (kg) that adult blue crabs is normally dispersed with a population mean (μ) that 0.8 kg and also a conventional deviation (σ) the 0.3 kg. How do we recognize this probability? First, us calculate the z score by instead of X with 1, the typical (μ) through 0.8 and standard deviation (σ) v 0.3. Us calculate ours z-score to it is in (1-0.8)/0.3=0.6667. We can then watch in our z table to determine the p(z>0.6667) is roughly 1-0.748 (pulled native the chart, somewhere between 0.7454 and also 0.7486) = 0.252. Therefore, based on our normality assumption, we conclude that the likelihood that a randomly selected adult blue crab weighs more than one kilogram is around 25.2% (the area shaded in blue).See more: Canelo Vs Ggg 2 Cancelled After Alvarez Pulls Out After Pending Suspension

The college student t Probability Distribution