Problem

Mercury Poisoning Historians and biographers have…

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Problem 45 Hard Difficulty

Life Expectancy According to the National Center for Health Statistics, life expectancy for a 70 -year-old African American male is 12.3 years. Assuming that from age 70 , the survival of African American males follows an exponential distribution, determine the following probabilities. Source: National Vital
Statistics Report.
a. The probability that a randomly selected 70 -year-old African American male will live beyond 90 years of age
b. The probability that a randomly selected 70 -year-old African American male will live between 10 and 20 more years

Answer

a. 0.1967
b. 0.2468

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Calculus 1 / AB

Finite Mathematics and Calculus with Applications

Chapter 18

Probability and Calculus

Section 3

Special Probability Density Functions

Discussion

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Video Transcript

Okay, So we're told that we have an exponentially distributed random variable with me enough 12.3. So our density function will be FX. Here. We want to know the probability the X is greater than 20 for the first part. So this is one minus probability. That X is less than 20 which will be one minus the integral from 0 to 20 of you to the negative X over 12.3, divided by 12.3. And so, if we evaluate, the central will get one minus one minus e to the negative 20/12 10.3. And if we plug this into a calculator, we will get about point 19 67 So this will be the first answer for this question. And if we do the second part, were asked the probability that X will be between 10 and 20. So this will be the probability that X is less than 20 minus the probability the X is less than 10. Um so we actually already calculated the probability that excess less than 20 right here, so, you know, that's one minus e to the negative, 20 over 12.3 and over here. This full done. Just be one minus eats the night of 10 over 12.3 on. So if we plug these into a calculator, we should get about 0.246 eight as final answer.

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