Respuesta :
Answer:
a. The probability that the time between the next two calls will be 45 seconds or less is 46%.
b. The probability that the time between the next two calls will be greater than 118.5 seconds is 19%.
Step-by-step explanation:
The cumulative density function of the exponential distribution for x≥0 is:
[tex]F(x;\lambda)=1-e^{-\lambda x}[/tex]
In this case,
[tex]\lambda=1/\mu=1/1.2 \,min^{-1}=\frac{1}{1.2} *\frac{1}{min}*\frac{1\,min}{60s}= \frac{1}{72} \, s^{-1}[/tex]
a) What is the probability that the time between the next two calls will be 45 seconds or less?
The probability that the time between the next two calls will be 45 seconds or less is 46%.
[tex]P(x\leq45)=1-e^{45/72}=1-0.54=0.46[/tex]
b) What is the probability that the time between the next two calls will be greater than 118.5 seconds?
The probability that the time between the next two calls will be 118.5 seconds or less is 19%.
[tex]P(x>45)=1-(1-e^{118.5/72})=e^{118.5/72}=0.19[/tex]
