The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with μ=9.4 inches and σ=1.6 inches. Please round z-scores to 2 decimal places and give probabilities to at least 4 decimal places. (a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)ANSWER: (b) Write the event ''a fish chosen has a length of over 7.4 inches'' in terms of X: (c) Find the probability of this event: (d) Find the probability that the length of a chosen fish was greater than 12.4 inches: (e) Find the probability that the length of a chosen fish was between 7.4 and 12.4 inches:
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 length, X, of a fish from a particular mountain lake in Idaho is normally distributed with μ=9.4 inches and σ=1.6 inches. Please round z-scores to 2 decimal places and give probabilities to at least 4 decimal places.
(a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)
ANSWER:
(b) Write the
(c) Find the probability of this event:
(d) Find the probability that the length of a chosen fish was greater than 12.4 inches:
(e) Find the probability that the length of a chosen fish was between 7.4 and 12.4 inches:
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