Question

According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fewer were never in a museum? Round to the nearest thousandth.

Answer 1

Solution:

Here, we have to use binomial distribution.

We are given n = 10, p = 0.15, q = 1 – p = 1 – 0.15 = 0.85

We have to find P(X≤2)

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X=x) = nCx*p^x*q^(n – x)

P(X=0) = 10C0*0.15^0*0.85^(10 – 0)

P(X=0) = 1*0.15^0*0.85^10

P(X=0) = 0.196874

P(X=1) = 10C1*0.15^1*0.85^(10 – 1)

P(X=1) = 10*0.15^1*0.85^9

P(X=1) = 0.347425

P(X=2) = 10C2*0.15^2*0.85^(10 – 2)

P(X=2) = 45*0.15^2*0.85^8

P(X=2) = 0.275897

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = 0.196874 + 0.347425 + 0.275897

P(X≤2) = 0.820196

Required probability = 0.820