The time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable T, the model here taking the probability that a butterfly survives for more than t days as 36 P(T > t) = For these problems, please ensure your answers are accurate to within 3 decimals. Part a) What is the probability that a butterfly will die within 6 days of emerging? Part b) If a large number of butterflies emerge on the same day, after how many days would you expect only 6 % to be alive? Part c) Calculate the mean lifetime of a butterfly after emerging from its chrysalis.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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The time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable T, the model here taking the probability that a butterfly
survives for more than t days as
36
P(T >t)
GE7, t>0.
(6+t)² »
For these problems, please ensure your answers are accurate to within 3 decimals.
Part a)
What is the probability that a butterfly will die within 6 days of emerging?
Part b)
If a large number of butterflies emerge on the same day, after how many days would you expect only 6 % to be alive?
Part c)
Calculate the mean lifetime of a butterfly after emerging from its chrysalis.
Transcribed Image Text:The time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable T, the model here taking the probability that a butterfly survives for more than t days as 36 P(T >t) GE7, t>0. (6+t)² » For these problems, please ensure your answers are accurate to within 3 decimals. Part a) What is the probability that a butterfly will die within 6 days of emerging? Part b) If a large number of butterflies emerge on the same day, after how many days would you expect only 6 % to be alive? Part c) Calculate the mean lifetime of a butterfly after emerging from its chrysalis.
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