Question

You have an opaque urn with eight balls in it. Of these eight balls, there are two balls with a 4 on them, there are four balls with a 5 on them, there is one ball with a 6 on it, and one ball with a 10 on it. Let X denote the random variable that takes on the values X = 4,5,6,10.

Find the:

a. mean

b. variance

c. standard deviation

d. skewness

e. kurtosis

f. median

g. mode

h. coefficient of variation for X ?

i. Find the value of the distribution function F(x) when x = 5.

Show your work in Excel without using the Descriptive Statistics command.

j. How much total probability is contained within two standard deviations of the mean?

Answer 1

X	(X - X̄)²
4	2.25
4	2.25
5	0.25
5	0.25
5	0.25
5	0.25
6	0.250
10	20.250

	X	(X - X̄)²
total sum	44	26.00
n	8	8

a)

mean =    ΣX/n =    44.000   /   8   =   5.5000

b)
                      
sample variance =    Σ(X - X̄)²/(n-1)=   26.0000   /   7   =   3.714

c)
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (26/7)   =       1.9272

d)

skewness using pearson coefficient of skewness,PC      
PC=3(mean-median)/std dev=       0.778312

f)

Median=0.5(n+1)th value =    4.5th
=   5.000

g)

mode= highest frequency data =    5

h)

coefficient of variation,CV=σ/µ=   0.350409

i)

F(x) = 4/8

= 0.5

j)

95% probability

Thanks in advance!

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