From the graph we can see that in the interval [0,1] the value of y is less than 1.
In the interval [1,2] the value of y value is 2 to 4.
In the interval [2,infinity) the graph is going up, and the value of y is greater than or equal to 4.
Therefore, the graph going up after y=4 above the line.
Therefore, the minimum y-value is 4 after which the exponential function will always be greater than the linear function.
Answer:
(a) The expected number of should a salesperson expect until she finds a customer that makes a purchase is 0.9231.
(b) The probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 0.058.
Step-by-step explanation:
Let<em> </em>the random variable <em>X</em> be defined as the number of customers the salesperson assists before a customer makes a purchase.
The probability that a customer makes a purchase is, <em>p</em> = 0.52.
The random variable <em>X</em> follows a Geometric distribution since it describes the distribution of the number of trials before the first success.
The probability mass function of <em>X</em> is:
The expected value of a Geometric distribution is:
(a)
Compute the expected number of should a salesperson expect until she finds a customer that makes a purchase as follows:
This, the expected number of should a salesperson expect until she finds a customer that makes a purchase is 0.9231.
(b)
Compute the probability that a salesperson helps 3 customers until she finds the first person to make a purchase as follows:
Thus, the probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 0.058.