Respuesta :
Answer:
a) The agent sells 37,500$ of insurance on an average day.
b) There is a 53.85% probability that the agent sells more than $40,000 of insurance on a particular day.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
The mean of this distribution is given by the following formula:
[tex]M = \frac{a+b}{2}[/tex]
For this problem, we have that:
[tex]a = 5000, b = 70000[/tex]
A. What amount of insurance does the agent sell on an average day?
[tex]M = \frac{5000 + 70000}{2} = 37500[/tex]
The agent sells 37,500$ of insurance on an average day.
B. Find the probability that the agent sells more than $40,000 of insurance on a particular day.
[tex]P(X \leq 40000) + P(X > 40000) = 1[/tex]
[tex]P(X > 40000) = 1 - P(X \leq 40000) = 1 - \frac{40000 - 5000}{70000 - 5000} = 0.5385[/tex]
There is a 53.85% probability that the agent sells more than $40,000 of insurance on a particular day.
