Discrete Random Variables we are working with commonly used

Discrete Random Variables

we are working with commonly used discrete and continuous distribution

In a large population 10% of the people have type B+ blood. At a blood donation center 20 people donate blood. What is the probability that exactly 5 of these people have B+ blood? What is the probability that at least 4 people have B+ blood? What is the expected value and standard deviation of people having B+ blood?

Solution

A)
Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    20      
p = the probability of a success =    0.1      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.031921361 [ANSWER]

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b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.1      
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   3   ) =    0.867046677
          
Thus, the probability of at least   4   successes is  
          
P(at least   4   ) =    0.132953323 [ANSWER]

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C)

E(x) = n p = 20*0.10 = 2 [ANSWER]

s(x) = sqrt(np(1-p)) = sqrt(20*0.10*(1-0.10)) = 1.341640786 [ANSWER]