The graph to the right is the uniform probability density function for a friend

Question

The graph to the right is the uniform probability density function for a friend who is x minutes late.

(a) Find the probability that the friend is between 5and 30
minutes late.

(b) It is 10 A.M. There is a 20%
probability the friend will arrive within how many minutes?

StartFraction 1 Over 30 EndFraction130

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The graph to the right is the uniform probability density function for a friend who is x minutes late.

(a) Find the probability that the friend is between 5and 30
minutes late.

(b) It is 10 A.M. There is a 20%
probability the friend will arrive within how many minutes?

StartFraction 1 Over 30 EndFraction130

Edit Coordinates... (0,0)

Explanation / Answer

Ans:

X is unoiformely ditributed between 0 and 30 min.

f(x)=1/(30-0)=1/30

F(x)=(x-a)/(b-a)=(x-0)/(30-0)=x/30

P(X<=x)=x/30

a)P(25<X<30)=P(X<30)-P(X<25)=(30/30)-(25/30)=5/30=1/6

b)

F(x)=0.2=x/30

x=0.2*30=6 minutes

c)P(x>=9)=1-(9/30)=21/30=7/10

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