find binomail probabilities 15-20 find the indicated probabilities if convenient

Question

find binomail probabilities 15-20 find the indicated probabilities if convenient use technolpgy or table 2 in appendix b to find the probabilities ?

a. Fair and Accurate News Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four.

b. Childhood Obesity Thirty-nine percent of U.S. adults think that the government should help fight childhood obesity. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who think that the government should help fight childhood obesity is (a) exactly two, (b) at least four, and (c) less than three.

Explanation / Answer

1. a. Fair and Accurate News Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four.

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 =    9      
p = the probability of a success =    0.6      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.250822656 [ANSWER]

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b)

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 =    9      
p = the probability of a success =    0.6      
x = our critical value of successes =    6      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   5   ) =    0.517390336
          
Thus, the probability of at least   6   successes is  
          
P(at least   6   ) =    0.482609664 [ANSWER]

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c)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    9      
p = the probability of a success =    0.6      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   2   ) =    0.025034752
          
Thus, the probability of at least   3   successes is  
          
P(more than   2   ) =    0.974965248 [ANSWER]

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