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Answer:
The probability that randomly selected road will be at least 25.8 cm long will be 48%.
Step-by-step explanation:
Given: uniform distribution with min and max values of 18 and 33 respectively.
To find : probability density for upper cumulative frequency i.e 25.8 at least means x25.8 upto 33 cm i.e the maximum limit of function.
Solution:
we have by definition , of uniform distribution
we get , probability density function defines as :
<em>F(x,a,b)= </em><em> </em>
=1/(33-18)=1/15=0.0667.
this is probability density function.
here the x=25.8 , a=18 and b=33
for lower cumulative frequency it defines as ;
P(x,a,b)= =25.8-18/33-18=0.52
for upper cumulative frequency it defines as ;
Q(x,a,b)=b-x/b-a=33-25.8/33-18=0.48
here at least 25.8 cm probability means it should be greater than a value(18cm) hence it is provided by the upper cumulative frequency
i.e. Q(x,a,b)=0.48
The probability that randomly selected road will be at least 25.8 cm long will be 48%.