Question

In a certain country tthe probability a randomly selected adult is literate is 0.84. Suppose we draw a simple random sample of 13 adults from this country.

a) What is the probability exactly 11 are literate?

Round your response to at least 3 decimal places

b) What is the probability more than 11 are literate?

Round your response to at least 3 decimal places.

Answer 1

Solution

Given that ,

p = 0.84

1 - p = 0.16

n = 13

a)

x = 11

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 11) = ((13! / 11! (13 - 11)!) * 0.84¹¹ * (0.16)^{13 - 11}

= 0.293

Probability = 0.293

b)

X > 11

P(X > 11) = P(X = 12 ) + P(X = 13 )

= ((13! / 12! (13 - 12)!) * 0.84¹² * (0.16)^{13 - 12} + ((13! / 13! (13 - 13)!) * 0.84¹³ * (0.16)^{13 - 13}

= 0.2567 + 0.1037

= 0.360

Probability = 0.360