In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 46% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 22 strikes. Find the following probabilities. (Round your answers to four decimal places.) (a) 12 or fewer fish were caught (b) 5 or more fish were caught (c) between 5 and 12 fish were caught
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!
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the
Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 46% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 22 strikes. Find the following probabilities. (Round your answers to four decimal places.)
(a) 12 or fewer fish were caught
(b) 5 or more fish were caught
(c) between 5 and 12 fish were caught
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