What is the most that a male penguin can weigh to be considered a chick? Given that a male penguin is a chick, what is the probability that it weighs less than 3000 grams?
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!
The distribution of weights of male Adelie penguins on Torgersen Island is assumed to be normal with a population mean weight of 4035 grams and a population standard deviation of 375 grams.
The bottom 1 percent of the weight distribution of male penguins are identified as chicks.
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What is the most that a male penguin can weigh to be considered a chick?
- Given that a male penguin is a chick, what is the probability that it weighs less than 3000 grams?
Provide your answers to these two questions with either a file upload OR in the following text box, clearly labeling each of the two parts.
Remember: for questions that involve calculations or derivations, you must show the setup of the problem (your thought process in terms of the statistical content). Your solutions must include the following, when appropriate:
- z-score
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