Given the following data for an imaginary superhero universe: Flying Telepathy Super Strength Female 53 19 26 Male 54 16 Distribution of Super Power by Gender What is the empirical probability that a randomly selected superhero will have telepathy?
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!
![**Data Analysis for an Imaginary Superhero Universe**
Given the following data for an imaginary superhero universe:
| | Flying | Telepathy | Super Strength |
|----------------|--------|-----------|----------------|
| Female | 53 | 19 | 26 |
| Male | 54 | 2 | 16 |
*Distribution of Super Power by Gender*
**Objective:**
Determine the empirical probability that a randomly selected superhero will have telepathy.
**Solution:**
To find the empirical probability, calculate the total number of superheroes with telepathy and divide by the total number of superheroes.
- Total superheroes with telepathy:
- Female with Telepathy: 19
- Male with Telepathy: 2
- Total with Telepathy = 19 + 2 = 21
- Total number of superheroes:
- Total Female: 53 + 19 + 26 = 98
- Total Male: 54 + 2 + 16 = 72
- Total Superheroes = 98 + 72 = 170
**Empirical Probability:**
\[ P(\text{Telepathy}) = \frac{\text{Total with Telepathy}}{\text{Total Superheroes}} = \frac{21}{170} \]
This fraction represents the probability that a superhero chosen at random will have telepathy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1658d937-8052-45d3-ba3f-7a589de5c533%2Fd8c49e6e-8916-4b4c-8406-26f6b609e985%2F26jotel_processed.jpeg&w=3840&q=75)
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