Answer:
a)
Mean [tex]\mu = \dfrac{1}{\lambda }= 1250[/tex]
[tex]\lambda = \dfrac{1}{1250}[/tex]
b)
[tex]P(X > 5000) = 0.0183[/tex]
c)
[tex]P(X > 1250) =0.3679[/tex]
Step-by-step explanation:
From the given information:
a.)
Mean [tex]\mu = \dfrac{1}{\lambda }= 1250[/tex]
[tex]\lambda = \dfrac{1}{1250}[/tex]
Let consider X to be a random variable that follows an exponential distribution; then:
P(X) = 1 - [tex]e^{- \lambda x}[/tex] since [tex]\lambda > 0[/tex]
b.)
The required probability that a random chosen customer would spend more than $5,000 can be computed as:
[tex]P(X > 5000) = 1 - \bigg [ 1 - e ^{- \dfrac{5000}{1250}} \bigg][/tex]
[tex]P(X > 5000) =e^ {-4[/tex]
[tex]P(X > 5000) = 0.0183[/tex]
c.)
[tex]P(X > 1250) = 1 - \bigg [ 1 - e ^{- \dfrac{1250}{1250}} \bigg][/tex]
[tex]P(X > 1250) =e ^{- 1[/tex]
[tex]P(X > 1250) =0.3679[/tex]
