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of the members of a Boy Scout troop, 15% have received the first aid merit badge

ID: 3386394 • Letter: O

Question

of the members of a Boy Scout troop, 15% have received the first aid merit badge. If 40 Boy Scouts are selected at random, find the probability that four or more will have first aid merit badge. of the members of a Boy Scout troop, 15% have received the first aid merit badge. If 40 Boy Scouts are selected at random, find the probability that four or more will have first aid merit badge. of the members of a Boy Scout troop, 15% have received the first aid merit badge. If 40 Boy Scouts are selected at random, find the probability that four or more will have first aid merit badge.

Explanation / Answer

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    40      
p = the probability of a success =    0.15      
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   ) =    0.130168762
          
Thus, the probability of at least   4   successes is  
          
P(at least   4   ) =    0.869831238 [ANSWER]

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