Respuesta :
Answer:
The answers to the questions are;
a-1. The rate parameter, λ is 0.0714 .
a-2. The standard deviation is 14.
b. No
c. The probability that a customer will show up in less than ten minutes is 0.5104.
d. The probability that nobody shows up for over forty minutes is 0.0574.
Step-by-step explanation:
a-1. The exponential distribution probability density function is given by
PDF = [tex]\lambda e^{-\lambda x}[/tex] and the cumulative distribution function is given by
CDF = [tex]1- e^{-\lambda x}[/tex]
Therefore the rate parameter the rate at which customers make purchases, that is the number of customers per minute
Therefore, the number of customers per minute = rate parameter = 1/14
The rate parameter, λ = 0.0714 .
a-2. In exponential distribution, which is the probability of the amount of time between two events where the rate of occurrence of events is constant, known as a Poisson point process, we have;
The mean = 1/λ = standard deviation
Therefore, the standard deviation is 14.
b. No
c. The probability that a customer will show up in less than ten minutes is given by the cumulative distribution function as follows
P (10<X) = [tex]1- e^{-\frac{10}{14} }[/tex] = 0.5104.
d. The probability that nobody shows up for over forty minutes is given by the area on the right of the exponential distribution function curve.
Therefore, we have
P (X>40) = [tex]1- (1- e^{-\frac{40}{14} })[/tex] = 0.0574
The probability that nobody shows up for over forty minutes is 0.0574.
