Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks). Round all answers to two decimal places. A. The mean of this distribution is B. The standard deviation is C. The probability that a person will be born at the exact moment that week 29 begins is P(x = 29) = D. The probability that a person will be born between weeks 5 and 18 is P(5 < x < 18) = E. The probability that a person will be born after week 30 is P(x > 30) = F. P(x > 17 | x < 21) = G. Find the 40th percentile. H. Find the minimum for the upper quartile.
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!
Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks). Round all answers to two decimal places.
A. The mean of this distribution is
B. The standard deviation is
C. The
D. The probability that a person will be born between weeks 5 and 18 is P(5 < x < 18) =
E. The probability that a person will be born after week 30 is P(x > 30) =
F. P(x > 17 | x < 21) =
G. Find the 40th percentile.
H. Find the minimum for the upper
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