Question

3) President Trump’s approval rating is 42%. Suppose that 10 people were chosen at random

a) Find the probability that 5 of the 10 people approve of the job President Trump is doing.

b) Find the probability that at most 3 of the 10 people approve of the job President Trump is doing.

c) Find the probability that at least 3 of 10 people approve of the job President Trump is doing.

Answer 1

a)

Here, n = 10, p = 0.42, (1 - p) = 0.58 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 5)
P(X = 5) = 10C5 * 0.42^5 * 0.58^5
P(X = 5) = 0.2162

b)

Here, n = 10, p = 0.42, (1 - p) = 0.58 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 3).
P(X <= 3) = (10C0 * 0.42^0 * 0.58^10) + (10C1 * 0.42^1 * 0.58^9) + (10C2 * 0.42^2 * 0.58^8) + (10C3 * 0.42^3 * 0.58^7)
P(X <= 3) = 0.0043 + 0.0312 + 0.1017 + 0.1963
P(X <= 3) = 0.3335

c)
Here, n = 10, p = 0.42, (1 - p) = 0.58 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 3).
P(X >= 3) = (10C3 * 0.42^3 * 0.58^7) + (10C4 * 0.42^4 * 0.58^6) + (10C5 * 0.42^5 * 0.58^5) + (10C6 * 0.42^6 * 0.58^4) + (10C7 * 0.42^7 * 0.58^3) + (10C8 * 0.42^8 * 0.58^2) + (10C9 * 0.42^9 * 0.58^1) + (10C10 * 0.42^10 * 0.58^0)
P(X >= 3) = 0.1963 + 0.2488 + 0.2162 + 0.1304 + 0.054 + 0.0147 + 0.0024 + 0.0002
P(X >= 3) = 0.8630