5.128 What is the probability of observing at least 60 cardinal birds in 2012? (Hint: Apply a continuity correction where appropriate.) The observers wish to identify a normal range for the number of cardinal birds observed per year. The normal range will be defined as the interval (L, U), where L is the largest integer ≤ 15th percentile and U is the smallest integer ≥ 85th percentile 5.130 What is the probability that the number of cardinal birds will be ≥ U at least once on Christmas day during the 10-year period 2012–2021? (Hint: Make the same assumptions as in Problem 5.128.)
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!
ANSWER OF PROBLEM 5.126 IS: (the mean number of cardinal birds per year is 61.71429.)
ANSWER OF PROBLEM 5.127 IS: (the standard deviation of cardinal birds per year observed from 2005 to 2011 is 9.59)
Suppose we assume that the distribution of the number of
cardinal birds observed per year is
that the true mean and sd are the same as the sample mean
and sd calculated in Problems 5.126 and 5.127.
5.128 What is the
cardinal birds in 2012? (Hint: Apply a continuity correction
where appropriate.)
The observers wish to identify a normal
will be defined as the interval (L, U), where L is the largest
integer ≤ 15th percentile and U is the smallest integer ≥
85th percentile
5.130 What is the probability that the number of cardinal
birds will be ≥ U at least once on Christmas day during the
10-year period 2012–2021? (Hint: Make the same assumptions as in Problem 5.128.)
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