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

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 :-

$\mu=\dfrac{a+b}{2}\\\\=\dfrac{60+5}{2}=32.5$

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

b) The probability density function = $\dfrac{1}{60-5}$

$=\dfrac{1}{55}$

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

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

$\dfrac{20}{55}=0.36363636\approx0.36$

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