You are watching: What happens to the graph of the normal curve as the mean increases?
What is a probability density duty (pdf)? (Hint: In thing 7, "pdf" does not only stand because that "probability distribution function" together it go in thing 6)
An equation used to compute probabilities of continuous random variables. That must satisfy the adhering to two properties:(1) the complete area under the graph of the equation end all feasible values the the arbitrarily variable should equal 1.(2) the heights that the graph the the equation must be higher than or same to "0" for all feasible values of the random variable. The is, the graph the the equation must lie ~ above or over the horizontal axis for all feasible values that the random variable.
If the feasible values that a uniform density duty go native 0 with n, what is the elevation of the rectangle?
the modefor symmetric distributions v a solitary peak, such as the regular distribution, the median = mean = mode. Since of this, the mean,
, is the high suggest of the graph of the distribution.
What worths of x are linked with the inflection points that a typical curve (continuous arbitrarily variables)?
because these space the points on the distribution curve where the curvature changes.
What happens to the graph (continuous random variables in a data set) once the average is shifted to the right? Left? What wake up to the same graph as soon as the typical deviation increases? Decreases?
when the median is change to the right, the normal circulation retains the very same shape and shifts to the right and also to the left once the typical shifts come the left.when the traditional deviation increases, the form of the normal distribution flattens out and also becomes wider. As soon as the standard deviation decreases, the normal circulation compresses and also becomes steeper.
1) The normal curve is symmetric about its mean,
2) due to the fact that mean = average = setting (for qualitatitve data), the regular curve has actually a single peak and the highest allude occurs at
3) The typical curve has actually inflection points at
4) The area under the regular curve is 1.5) The area under the regular curve come the appropriate of
equals the area under the common curve come the left of
, which equates to 0.5.6) together "x" rises without tied (gets larger and larger), the graph approaches, but never reaches, the horizontal axis. As "x" decreases without bound (gets an ext and an ext negative), the graph approaches, however never reaches, the horizontal axis.7) The Empirical Rule:Approximately 68% the the area under the normal circulation curve is between
, approximately 95% of the area is between
, and also approximately 99.7% of the area is between
Suppose the a arbitrarily variable X is normally spread with mean
and typical deviation
. Offer two representations for the area under the typical curve for any type of interval of values of the arbitrarily variable X.
1) The proportion of the population with the characteristic described by the interval of values,or2) The probability the a randomly selected individual from the populace will have actually the characteristic described by the expression of values.
7.2 (small data sets)A normal probability plot is...
...a graph that plots observed data versus normal scores.
7.2 (small data sets)A typical score is...
...the expected z-score the the data value, assuming the the circulation of the random variable is normal. The expected z-score of an observed value relies on the number of observations in the data set.
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7.2 (small data sets)What are the four steps to follow when drawing a common Probability Plot by hand? What is the difference in between a z-score and also a fi-score?
Step 1 - arrange the data in ascending order.Step 2 - Compute fi=i−0.375n+0.25 where i is the index (the position of the data value in the bespeak list) and n is the variety of observations. The meant proportion the observations less than or equal to the ith data value is fi.Step 3 - discover the z-score equivalent to fi from Table V.Step 4 - Plot the observed values on the horizontal axis and also the corresponding expected z-scores on the vertical axis.The worth of fi represents the expected area come the left the the ith observation when the data come native a population that is generally distributed. This is similar to the idea of recognize the area come the left that an intended z-score under a normal circulation (observations vs prediction based upon the average).Once we recognize each fi, we discover the z-scores matching to f1 (represents z1 value for observed values), f2 (represents z2 because that observed values), and so on.
7.2 (small data sets)Values of normal random variables and also their z-scores are linearly related (x=μ+zσ), so a plot of observations of common variables versus their expected z-scores will be linear. We conclude the following:T or FIf sample data are taken native a populace that is generally distributed, a normal probability plot of the observed values versus the expected z-scores will certainly be around linear.True False
7.2 (small data sets)T or FIf the linearly correlation coefficient in between the it was observed values and expected z-scores is greater than the an essential value found in Table VI, then it is reasonable come conclude the the data might come from a population that is normally distributed.True False