Blood type AB is found in only 3 of the population If 280 pe

Blood type AB is found in only 3% of the population†. If 280 people are chosen at random, find the probability of the following.

(a) 5 or more will have this blood type

(b) between 5 and 10 will have this blood type

Solution

A.

To get this, we have to get the probability of \"4 or less\", then get the complement.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    280      
p = the probability of a success =    0.03      
x = the number of successes =    4      
          
Then the cumulative probability is          
          
P(x <=   4   ) =    0.0758194

THus, the probability of 5 or more is

P(5 or more) = 0.9241806 [ANSWER]

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B.

To get this, note that

P(between 5 and 10) = P(at most 10) - P(at most 4)

We got P(at most 4) = 0.0758194

Using tables/technology, we can also get that

P(at most 10) = 0.776967665

Thus,

P(between 5 and 10) = 0.701148265 [ANSWER]