9) The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are in hundreds of calories): f(x) ={32(x- 2)(6-x) for2
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!
![**Topic: Solar Radiation Probability in Tampa, Florida**
The effectiveness of solar-energy heating units is determined by the level of radiation available from the sun. During a typical October in Tampa, Florida, the daily total solar radiation is represented by a probability density function. This function measures the likelihood of different levels of radiation in hundreds of calories:
\[
f(x) =
\begin{cases}
\frac{3}{32}(x-2)(6-x) & \text{for } 2 \leq x \leq 6 \\
0 & \text{elsewhere}
\end{cases}
\]
**Explanation of the Function:**
- The probability density function \( f(x) \) is defined for \( x \), where \( x \) ranges from 2 to 6. This range corresponds to solar radiation values between 200 and 600 calories.
- \( f(x) = \frac{3}{32}(x-2)(6-x) \) describes the likelihood of observing a specific level of radiation within this range.
- Outside the range of 2 to 6 inclusive, the probability is zero, meaning no solar radiation levels are expected in hundreds of calories beyond this range during a typical October day.
**Objective:**
- Calculate the probability that solar radiation exceeds 300 calories (i.e., greater than 3 in the function scale) on a typical October day in Tampa.
This involves integrating the probability density function from 3 to 6, as this provides the probability of radiation values exceeding 300 calories.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25623933-adaa-4674-a5a0-c7198921edd9%2F0aa6cd0a-84cb-4c5b-bdf8-5f24e6a295e1%2F9djw79x_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
