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.
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)!) * px * (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
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