normal type

Examples of normal type in the following topics:

• Probability Histograms and the Normal Curve

  • Many different types of distributions can be approximated by the normal curve.
  • The occurrence of the normal distribution in practical problems can be loosely classified into three categories: exactly normal distributions, approximately normal distributions, and distributions modeled as normal.
  • How can we tell if data in a probability histogram are normal, or at least approximately normal?
  • A normal probability plot is a graphical technique for normality testing--assessing whether or not a data set is approximately normally distributed.
  • This is a sample of size 50 from a normal distribution, plotted as a normal probability plot.

• Change of Scale

  • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
  • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
  • In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution.
  • Some types of normalization involve only a rescaling, to arrive at values relative to some size variable.
  • Explain the significance of normalization of ratings and calculate this normalization

• Summary of Formulas

  • α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.
  • β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.
  • Single population mean, known population variance (or standard deviation): Normal test.

• Benefits

  • State how distribution-free tests can avoid an inflated Type I error rate
  • Most tests based on the normal distribution are said to be robust when the assumption of normality is violated.
  • Although this sounds like a good thing because the Type I error rate is lower than the nominal rate, it has a serious downside: reduced power.
  • Tests assuming normality often have low power for leptokurtic distributions.
  • Because distribution-free tests do not assume normality, they can be less susceptible to non-normality and extreme values.

• The Standard Normal Curve

  • The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
  • If the mean ($\mu$) and standard deviation ($\sigma$) of a normal distribution are 0 and 1, respectively, then we say that the random variable follows a standard normal distribution.
  • This type of random variable is often denoted by $Z$, instead of $X$.
  • Part one: Since the height of women follows a normal distribution but not a standard normal, we first need to standardize.
  • Explain how to derive standard normal distribution given a data set

• Chemical Composition of Urine

  • Normal chemical composition of urine is mainly water content, but also includes nitrogenous molecules, such as urea, as well as creatinine and other metabolic waste components.
  • Some of the more common types of abnormal urine include:
  • Describe how normal urine consists of water, urea, salts and pigment

• Examining the Central Limit Theorem

  • The distribution of is approximately normal.
  • For example, the normal approximation for the log-normal example is questionable for a sample size of 30.
  • There are two outliers, one very extreme, which suggests the data are very strongly skewed or very distant outliers may be common for this type of data.
  • If a data set has prominent outliers, or such observations are somewhat common for the type of data under study, then it is useful to collect a sample with many more than 30 observations if the normal model will be used for ¯ x.
  • The dashed red lines show normal distributions.

• Shapes of Sampling Distributions

  • The overall shape of a sampling distribution is expected to be symmetric and approximately normal.
  • The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central; and where types of departure from this include:
  • A normal distribution is usually regarded as having short tails, while a Pareto distribution has long tails.
  • As previously mentioned, the overall shape of a sampling distribution is expected to be symmetric and approximately normal.
  • Sample distributions, when the sampling statistic is the mean, are generally expected to display a normal distribution.

• t Distribution

  • State the difference between the shape of the t distribution and the normal distribution
  • In the introduction to normal distributions it was shown that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean.
  • Fortunately, the way to work out this type of problem was solved in the early 20th century by W.
  • The t distribution approaches the normal distribution as the degrees of freedom increase.
  • The corresponding values for the normal distribution are 1.96 and 2.58 respectively.

• Normal Genitourinary Microbiota

  • Those that are expected to be present and that under normal circumstances do not cause disease, but instead participate in maintaining health, are deemed members of the normal flora.
  • Their role forms part of normal, healthy human physiology; however, if microbe numbers grow beyond their typical ranges (often due to a compromised immune system) or if microbes populate atypical areas of the body (such as through poor hygiene or injury), disease can result.
  • Normal flora bacteria can act as opportunistic pathogens at times of lowered immunity.The vaginal microflora consist mostly of various lactobacillus species .