SOLUTION: Question 2. For each of the following probability distributions, classify the problem as a normal distribution, binominal distribution, geometric distribution, or Poisson distr

Question 1105340: Question 2.
For each of the following probability distributions, classify the problem as a normal distribution, binominal distribution, geometric distribution, or Poisson distribution, then answer the question.

a) A surgical technique is performed on 50 patients. You are told there is a 60% chance of success. Find the probability that the surgery is successful 32 times.

b) A surgical technique is performed on 50 patients. You are told there is a 60% chance of success. Find the probability that the surgery is successful at least 32 times.
Binominal Distribution

c) The probability that a student passes the written test for a private pilot�s license is 0.75. What is the probability that a student will fail on the first attempt and pass on the second attempt? BINOMIAL

d) In Tampa, Florida, the mean number of days in July with 0.01 inch or more precipitation is 16. What is the probability that Tampa has 20 day with 0.01 inch or more precipitation next July?
POISSON

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The first is 50C32*0.6^32*0.4^18. This is 0.0987
The second uses the mean and sd of 30 (np) and variance 12 (np*(1-p)) so sd is 3.46 (sqrt var)
using continuity correction factor want z=(31.5-30)/3.46 or +0.4335. This probability is 0.3323.
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c) This is 0.25*0.75=0.1875.
d) If one uses the Poisson (I would probably use the binomial, since the probabilities would be known) the parameter is 16 and 20 is wanted. Therefore, lambda is 16 and x is 20.
e^(-16)*16^20/20!=0.0559
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