The length of time t (in seconds) that it takes the body to react to the injection of a particular drug has the probability density function f(t) = 392 where 1 < t < 14. 195t3 ' Step 1 of 2: What is the probability that it will take at least 6 seconds for the body to react to the drug? Enter your answer as an exact expression or rounded to 4 decimal places.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![### Reaction Time to Drug Administration
The length of time \( t \) (in seconds) that it takes the body to react to the injection of a particular drug has the probability density function:
\[ f(t) = \frac{392}{195t^3}, \text{ where } 1 \le t \le 14. \]
**Step 1 of 2:** What is the probability that it will take at least 6 seconds for the body to react to the drug? Enter your answer as an exact expression or rounded to 4 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65a8e990-5360-43af-b3a8-27c1c40fb79a%2F28b95502-bd30-4865-9b05-216449a5ff7a%2Fgv7mgv_processed.png&w=3840&q=75)
![The length of time \( t \) (in seconds) that it takes the body to react to the injection of a particular drug has the probability density function
\[ f(t) = \frac{392}{195t^3}, \quad \text{where } 1 \leq t \leq 14. \]
**Step 2 of 2:** What is the average waiting time for the body to react? Enter your answer as an exact expression or rounded to 2 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65a8e990-5360-43af-b3a8-27c1c40fb79a%2F28b95502-bd30-4865-9b05-216449a5ff7a%2F2bbm9a_processed.png&w=3840&q=75)
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