Let y denote the number of broken eggs in a randomly selected carton ofone dozen eggs. Suppose that the probability distribution of y is asfollows: y 0 1 2 3 4 p(y) 0.65 0.20 0.10 0.04 ? a. Only yvalues of 0, 1, 2, 3, and 4 have positive probabilities. Whatis p(4)? (Hint: Consider the properties of a discrete probabilitydistribution.)b. How would you interpret p(1) = 0.20? c. Calculate P(y ≤ 2) the probability that the carton contains at mosttwo broken eggs, and interpret this probability.d. Calculate P(y < 2), the probability that the carton contains fewerthan two broken eggs. Why is this smaller than the probability inPart (c)?
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!
Let y denote the number of broken eggs in a randomly selected carton of
one dozen eggs. Suppose that the
follows:
| y | 0 | 1 | 2 | 3 | 4 |
| p(y) | 0.65 | 0.20 | 0.10 | 0.04 | ? |
a. Only yvalues of 0, 1, 2, 3, and 4 have positive probabilities. What
is p(4)? (Hint: Consider the properties of a discrete probability
distribution.)
b. How would you interpret p(1) = 0.20?
c. Calculate P(y ≤ 2) the probability that the carton contains at most
two broken eggs, and interpret this probability.
d. Calculate P(y < 2), the probability that the carton contains fewer
than two broken eggs. Why is this smaller than the probability in
Part (c)?
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