The number of ants per acre in the forest is normally distributed with a mean of 43,000 and a standard deviation of 12,222. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(----,----) b. Find the probability that a randomly selected acre in the forest has fewer than 57,110 ants. (------) c. Find the probability that a randomly selected acre has between 44,908 and 53,418 ants. (-------) d. Find the first quartile. (-------) ants (round your answer to a whole number)
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 number of ants per acre in the forest is
a. What is the distribution of X? X ~ N(----,----)
b. Find the probability that a randomly selected acre in the forest has fewer than 57,110 ants. (------)
c. Find the probability that a randomly selected acre has between 44,908 and 53,418 ants. (-------)
d. Find the first
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