Stats

• Continuous probability distribution - is a distribution consisting of observations that are measured on a continuous scale.
• The graph of a probability distribution for a continuous random variable X is a smooth curve. The curve is a function of X, denoted by f, and is also called a probability density function, a frequency function, or a probability distribution.
• Normal Distribution - the most important and most widely used among continuous distributions in Statistics.
• Normal Distribution - is often used in the natural and social sciences.
• Abraham de Moivre - an 18th century statistician, first developed the normal distribution as an approximation to the binomial distribution.
• Karl Gauss - also developed the concept of the normal curve from his study of errors of repeated measurements of objects. Thus, the normal distribution is sometimes referred to as the normal curve of errors or the Gaussian distribution.
• • The graph of the normal

  distribution is bell-shaped and extends indefinitely in both directions.
• The normal distribution is perfectly symmetric about the mean y and its spread is determined by the value of its standard deviation o
• The mean, median and mode coincide at the center.
• The curve comes closer and closer

  to the horizontal axis without touching it no matter how far it goes away from the mean.
• The total area under the curve is 1.

  Thus, it represents the probability, proportion, or percentage associated with specific sets of measurement values.
• Standard Normal Table - also called the unit normal table or Z-table
• Standard Normal Table - is a table for the values of z calculated mathematically, and these are the values from the cumulative normal distribution function.
• Standard Normal Table - is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution.
• • The units marked on the horizontal axis are denoted by z and are called z-values or z-scores. The value of z tells you how many standard deviations above or below the mean the corresponding value of X is.
• Standard score or z-score - measures how many standard deviation a given value (x) is above or below the mean.
• Standard score or z-score - are

  useful in comparing observed values. A positive z-score indicates that the score or observed value is above the mean, whereas a negative z-score indicates that the score or observed value is below the mean.
• In many real-world applications, a continuous random variable may have a normal distribution with values of the mean and standard deviation that are not equal to 0 and 1, respectively. The units of the random variable are given in terms of X.
• This being the case, the first step

  is to convert the given normal distribution into the standard normal distribution. That is the x-scale is converted to the z-scale. This process is called standardizing a normal distribution.