Answer: a) $ 32500
b)0.36
Step-by-step explanation:
Given : The amount of insurance (in thousands of dollars) sold in a day by a particular agent is uniformly distributed over the interval [5, 60].
a) The mean value for continuous uniform distribution function with interval [a,b] is given by :-
[tex]\mu=\dfrac{a+b}{2}\\\\=\dfrac{60+5}{2}=32.5[/tex]
Hence, the amount of insurance does the agent sell on an average day = $ 32500.
b) The probability density function = [tex]\dfrac{1}{60-5}[/tex]
[tex]=\dfrac{1}{55}[/tex]
Required interval =[40,60]=60-40=20
Now, the probability that the agent sells more than $40,000 of insurance on a particular day :-
[tex]\dfrac{20}{55}=0.36363636\approx0.36[/tex]
Hence, the probability that the agent sells more than $40,000 of insurance on a particular day = 0.36
