Question

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.

Answer 1

Answer: a) $ 32500

b)0.36

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 :-

`\mu=(a+b)/(2)\\\\=(60+5)/(2)=32.5`

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

b) The probability density function =
`(1)/(60-5)`

`=(1)/(55)`

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

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

`(20)/(55)=0.36363636\approx0.36`

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