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. what amount of insurance does the agent sell on an average day? b. find the probability that the agent sells more than $40,000 of insurance on a particular day.

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 :-

Hence, the  amount of insurance does the agent sell on an average day = $ 32500.

b) The probability density function =

Required interval =[40,60]=60-40=20

Now, the probability that the agent sells more than $40,000 of insurance on a particular day :-

Hence, the probability that the agent sells more than $40,000 of insurance on a particular day = 0.36

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