A Java applet named Visualizing Normal Curve can be found in the following link:

Question

A Java applet named Visualizing Normal Curve can be found in the following link:

http://homepage.stat.uiowa.edu/~mbognar/applets/normal.html

Use this applet to solve the following problem. Make sure to take a snapshot for every part of the question:

Given that x is a normally distributed random variable with a mean of 10 and a standard deviation of 2,

(1) Find the probability that x lies between 11 and 13.6.

(2) For the same value of x and the mean, increase the standard deviation gradually and show how does the curve change?

(3) For the same value of x and the mean, decrease the standard deviation gradually and show how does the curve change?

(4) State your conclusions.

Explanation / Answer

1) by putting those value we get P(11<x<13.6)=P(x<13.6)-P(x<11)=.273

2) when we increase the sd curve the density at mode that is f(x) at mode is lower and lower and the tails of the curve spreading gradually

3) when we decrease the sd then value of f(x ) at modal value gradually increases and the curve much tighter than the previous position....

4) in the ist case as we increasing the sd then spread ness is increasing thats why the tails are spreading to incate that the spreadness or the dispersion of the distribution is shifting to higher value ...but in the next case as we decrease the sigma that means the dispersion is gradually lower from the previous one and the curve is gradually thight (i.e dispersion is slowly dicreasing ) and the value of the density increasing which is also clear from its mathematical formula .

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