Question

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.

Answer 1

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) = ⁿC_x p^x (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)]