You are watching: What happens to the graph of the normal curve as the standard deviation decreases?
What is a probability density function (pdf)? (Hint: In chapter 7, "pdf" go not just stand for "probability distribution function" together it walk in chapter 6)
An equation used to compute probabilities of constant random variables. That must fulfill the following two properties:(1) the full area under the graph the the equation end all feasible values of the random variable need to equal 1.(2) the heights the the graph of the equation should be better than or equal to "0" because that all feasible values that the arbitrarily variable. That is, the graph that the equation need to lie top top or over the horizontal axis because that all feasible values of the arbitrarily variable.
If the feasible values the a uniform density role go indigenous 0 with n, what is the height of the rectangle?
the modefor symmetric distributions with a solitary peak, such as the common distribution, the typical = typical = mode. Because of this, the mean,
, is the high allude of the graph the the distribution.
What worths of x are associated with the inflammation points the a regular curve (continuous random variables)?
because these room the points on the distribution curve whereby the curvature changes.
What wake up to the graph (continuous random variables in a data set) when the mean is shifted to the right? Left? What wake up to the very same graph when the typical deviation increases? Decreases?
when the typical is shifted to the right, the normal distribution retains the same shape and shifts to the right and to the left as soon as the average shifts come the left.when the standard deviation increases, the shape of the normal distribution flattens out and also becomes wider. As soon as the traditional deviation decreases, the normal circulation compresses and also becomes steeper.
1) The typical curve is symmetric around its mean,
2) since mean = typical = setting (for qualitatitve data), the typical curve has actually a single peak and the highest allude occurs at
3) The normal curve has actually inflection points at
4) The area under the common curve is 1.5) The area under the normal curve to the best of
equals the area under the regular curve come the left of
, which equals 0.5.6) together "x" boosts without bound (gets larger and also larger), the graph approaches, yet never reaches, the horizontal axis. Together "x" decreases there is no bound (gets much more 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 distribution curve is between
, around 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 traditional deviation
. Give two representations for the area under the regular curve for any kind of interval of values of the arbitrarily variable X.
1) The proportion the the populace with the characteristic defined by the expression of values,or2) The probability the a randomly selected individual from the populace will have actually the characteristic described by the interval of values.
7.2 (small data sets)A typical probability plot is...
...a graph that plots observed data versus normal scores.
7.2 (small data sets)A regular score is...
...the expected z-score of the data value, assuming that the circulation of the arbitrarily variable is normal. The expected z-score the an observed value depends on the variety of observations in the data set.
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7.2 (small data sets)What space the four steps to follow when illustration a normal Probability Plot through hand? What is the difference in between a z-score and also a fi-score?
Step 1 - kinds the data in ascending order.Step 2 - Compute fi=i−0.375n+0.25 where i is the index (the place of the data worth in the ordered list) and n is the variety of observations. The intended proportion the observations less than or equal to the ith data worth is fi.Step 3 - uncover the z-score equivalent to fi from Table V.Step 4 - Plot the observed worths on the horizontal axis and also the equivalent expected z-scores ~ above the vertical axis.The value of fi represents the expected area come the left of the ith monitoring when the data come from a populace that is usually distributed. This is as with the idea of finding the area come the left of an meant z-score under a normal distribution (observations vs prediction based on the average).Once we recognize each fi, we find the z-scores corresponding to f1 (represents z1 worth for observed values), f2 (represents z2 because that observed values), and so on.
7.2 (small data sets)Values of normal random variables and their z-scores room linearly related (x=μ+zσ), so a plot of monitorings of regular variables against their expected z-scores will certainly be linear. We conclude the following:T or FIf sample data are taken from a population that is usually distributed, a common probability plot of the observed values versus the expected z-scores will certainly be roughly linear.True False
7.2 (small data sets)T or FIf the linearly correlation coefficient in between the observed values and also expected z-scores is better than the vital value uncovered in Table VI, then it is reasonable come conclude that the data can come indigenous a population that is typically distributed.True False