Question

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 45% of strikes (while trolling)
resulted in a catch. Suppose that on a given day a fleet of fishing
boats got a total of 27 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

Answer #1

X ~ Bin ( n , p)

Where n = 27 , p = 0.45

Mean = n p = 27 * 0.45 = 12.15

Standard deviation = sqrt [ n p ( 1 - p) ]

= sqrt [ 27 * 0.45 ( 1 - 0.45) ]

= 2.5851

Using normal approximation,

P(X < x) = P(Z < ( x - Mean) / SD)

a)

Using continuity correction,

P(X <= 12) = P(Z < (12.5 - 12.15) / 2.5851)

= P(Z < 0.14)

= **0.5557**

b)

P(X >= 5) = P ( Z > ( 5.5 - 12.15) / 2.5851)

= P(Z > -2.57)

= P(Z < 2.57)

= **0.9949**

c)

P( 5 <= X <= 12) = P( 4.5 < X < 12.5)

= P(X < 12.5) - P(X < 4.5)

= P(Z < ( 12.5 - 12.15) / 2.5851) - P(Z < (4.5 - 12.15) / 2.5851)

= P(Z < 0.14) - P(Z < -2.96)

= 0.5557 - 0.0015

= **0.5542**

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 23 strikes. Find the following probabilities.
(Round your answers to four...

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 27 strikes. Find the following probabilities.
(Round your answers to four...

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 41% 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...

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 26 strikes. Find the following probabilities. (Round
your answers to four...

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 39% of strikes (while trolling)
resulted in a catch. Suppose that on a given day a fleet of fishing
boats got a total of 21 strikes. Find the following probabilities.
(Round your answers to four...

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 39% of strikes (while trolling)
resulted in a catch. Suppose that on a given day a fleet of fishing
boats got a total of 30 strikes. Find the following probabilities.
(Round your answers to four...

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 42% 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...

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 45% of strikes (while trolling)
resulted in a catch. Suppose that on a given day a fleet of fishing
boats got a total of 21 strikes. Find the following probabilities.
(Round your answers to four...

Ocean fishing for billfish is very popular in the Cozumel region
of Mexico. In the Cozumel region about 39% 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

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 20 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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