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A random number generator picks a number from one to nine in a uniform manner.

a. X ~ _________

b. Graph the probability distribution.

c. f(x) = _________

d. μ = _________

e. σ = _________

f. P(3.5 < x < 7.25) = _________

g. P(x > 5.67)

h. P(x > 5|x > 3) = _________

i. Find the 90th percentile

Short Answer

Expert verified

a. X~υ1,9

b.

c.

fx=180,1<x<9

d. μ=5

e.σ=2.31

f.P(3.5<x<7.25)=0.4688

g.P(x>5.67)=0.41625

h.P(x>5|x>3)=0.67

i. The 90th percentile is 8.2

Step by step solution

01

 Definition of measured variables 

The measurement variable means the expressions of some types of measurements which has an associated number.

02

Findings the results of measured variables 

a. Uniform of all data

X~U(1,9)

The height of probability distribution

b. the probability distribution function is

localid="1649324054718">f(x)=1b-aa=1b=53f(x)=19-1=18

The height of the distribution function= 1/8

Graph the probability distribution

c. The formulation of the

f(x)=1b-aa<X<b00forotherwisef(x)=181<X<800forotherwise

d. The mean value is

μ=a+b2=1+92=5

Then, the required value is 5

e. The standard deviation

localid="1649328736962" σ=b-a212σ=9-1212=2.31

Then, the required value is 2.31.

f. The required probability is as below:

localid="1649328744005" P(3.5<x<7.25)=base×height=(7.25-3.5)×18=0.4688

Then, the required value is 0.4688

g. The required probability is as below:

P(x>5.67)=base×height=(9-5.67)×18=0.41625

Then, the required value is 0.41625

h. The required probability is calculated as below:

P(x>5|x>3)=base×height=(9-5)×19-3=0.67

Therefore, the required value is 0.67

i. The 19th percentile of the data can be calculated as below:

For 90 percentile

localid="1649328754478" P(x<k)=base×height0.90=(k-1)×18k=8.2

The value of the 90th percentile is 8.2

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