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 40% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 29 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
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 40% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 29 strikes. Find the following probabilities. (Round your answers to four decimal places.)
(b) 5 or more fish were caught
(c) between 5 and 12 fish were caught
(a)
Obtain the probability that 12 or fewer fish were caught.
The probability that 12 or fewer fish were caught is obtained below as follows:
Let X denotes the number of fish were caught which follows binomial distribution with the probability of success 0.40 and the sample size of 29 has strikes selected.
Since, the value for np is greater than 5 and the value of nq is not greater than 5 it can be concluded that the normal curve cannot be used as an approximation to the binomial probability.
The mean and standard deviation are obtained below:
The required probability is
The probability that 12 or fewer fish were caught is 0.6331.
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