**Please answer all six questions** Question #1: three parts Question #2: three

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**Please answer all six questions**
Question #1: three parts
Question #2: three parts
Question #3: four parts
Question #4: four parts
Question #5: one part
Question #6: two parts

1. 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 probabilitles. Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 48% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 25 strikes, Find the following probabilitles. (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 2. Let x be a random varlable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with 7050 and estimated standard deviation = 2650. A test result of x

Explanation / Answer

1) p = 0.48 , n = 25

E(X) = np = 25*0.48 = 12

sd(X) = sqrt(npq) = sqrt(25*0.48*0.52) = 2.4979991

Z = (X - 12)/2.4979991

P(X < = 12)

P(X< 12.5) continuity correction

=P (Z<0.2)=0.5793

b)

P(X>=5)

=P(X > 4.5)

=P (Z>3)=0.9987

c) P( 5 <= <X < = 12)

=P(4.5 <X< 12.5)

=P ( 3<Z<0.2 )=0.578

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