In this problem, first you will explore the more general Standard Normal distrib

Question

In this problem, first you will explore the more general Standard Normal distribution N~(, 2) .
a) Create a 5 number summary (min, Q1, Q2, Q3, max) for the Standard Normal distribution. If a number is undefined, briefly explain why. Then create the (mean, standard deviation) pair of parameters. b) Using the results from a) and the definition of an outlier, create a box plot for the Standard Normal distribution. and show the boundaries for outliers as vertical dashed lines. Sketch the whiskers as if the points Q0.01, Q0.05, Q0.95, Q0.99 are part of the data set. Since you don’t have data, use the theoretical values for constructing the box plot.
c) Graph the density function.

Explanation / Answer

Using MINITAB, generate the random sample from standard normal distribution

Sample
   -1.01884    1.58631   -0.14137   -0.59837   -1.12329    0.92965   -1.14177
   -1.35380   -0.09747    0.17159    0.11323   -0.01183   -1.01990    0.16473
   -1.38719    0.91926    0.71422   -0.49623    0.99470   -0.81959    1.10643
   -0.52342    0.66760    0.14830   -0.58485    2.10004    0.83022   -2.00514
   -1.43536   -1.06674

a]

5 number summary

Minimum = -2.005

Q1 = -1.032

Q2 = -0.119

Q3 = 0.743

Maximum = 2.100

mean = -0.146 and standard deviaton = 1.008

b]

Outliers: An outliers are an observations that lies an abnormal distance from other values in a random sample from a population.

boundaries for outliers: if a data point is below Q1 – 1.5×IQR or above Q3 + 1.5×IQR, it is viewed as being too far from the normal values.

Where IQR = Q3 - Q1 = 0.743 - (-1.032) = 0.743 + 1.032 = 1.775

Lower limit: -1.032 - 1.5*1.775 = -3.6945

Upper limit: 0.743 + 1.5*1.775 = 3.4055

In our sampe there is outliers. that is all the points are within above limits

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