57% of U.S. adults oppose special taxes on junk food and soda. You randomly select 12 U.S. adults. Find the probability that at least 5 of the people you have selected oppose special taxes on junk food and soda. Show all work.
Let X be number of people you have selected oppose special taxes on junk food and soda.
Here, X ~ Binomial ( n = 12, p = 0.57)
probability mass function of X is,
P(X = x) = nCx px (1 - p)n-x
We want to find, P(X >= 5)
P(X >= 5)
= 1 - P(X < 5)
= 1 - P(X <= 4)
= 1 - BINOMDIST(4, 12, 0.57, 1)
= 0.91313988
=> P(X >= 5) = 0.91313988
=> P(X >= 5) = 0.9131 ( rounded to 4 decimal places)
Therefore, the probability that at least 5 of the people you have selected oppose special taxes on junk food and soda is 0.9131
Note:
Another way is,
P(X >= 5) = 1 - P(X < 5)
=> P(X >= 5) = 1 - [ P(X=0)+ P(X=1) + P(X=2)+ P(X=3) + P(X=4)]
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