Question

On a certain large Florida beach, in March 80% of the people on the beach are from other states. Suppose we take a sample of 20 people from this beach and count the number of people from other states.

a) What is the probability we will find at least 12 people from other states?

b) What is the probability we will find 15 to 17 people from other states?

c) Would we be surprised to find fewer than 10 people from other states in our sample? (i.e, would this be a “low probability” result?)

Answer 1

Solution:-

p = 0.80, n = 20

a) The probability we will find at least 12 people from other states is 0.99002

x = 12

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 12) = 0.99002

b) The probability we will find 15 to 17 people from other states is 0.5981.

x₁ = 15

x₂ = 17

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(15 < x < 17) = P(x > 15) - P(x > 17)

P(15 < x < 17) = 0.8042 - 0.20608

P(15 < x < 17) = 0.5981

c) Yes, we would be surprised to find fewer than 10 people from other states in our sample.

x = 10

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x < 10) = 0.00056

Yes, it would be low probability.