Question

Lifespan of dolphins using continuous probability model. The probability that a selected male . 30 lives past the age x is exp 2592 It is known that Dolphins live past 10 years. If that information is known, (a) what is the probability that a randomly chosen dolphin will live past 6 years (b) what is the probability that a random ly chosen dolphin will live between 5 and 12 years (c) what is the probability that the dolphin will will not live past 12 years?

Answer 1

a)P(live past 6 years given live past 10 years)=P(X>6|X>10)=P(X>6 and X>10)/P(X>10)

=P(X>10)/P(X>10)=1

b)

P(5<X<12|X>10)=P(10<X<12)/P(X>10)=(P(X<12)-P(X<10))/P(X>10)

=((1-exp(-12²/2592)-(1-exp(-10²/2592))/(exp(-10²/2592)=(0.0540-0.0378)/0.9622=0.0168

c)

P(X<12|X>10)=P(10<X<12)/P(X>10)=(P(X<12)-P(X<10))/P(X>10)

=((1-exp(-12²/2592)-(1-exp(-10²/2592))/(exp(-10²/2592)=(0.0540-0.0378)/0.9622=0.0168