A study indicates that 40% of American teenagers have tattoos. You randomly sample 25 teenagers. Find the probability that more than 6 will have tattoos.
Round your answer to 4 decimal places.
Given : n = 25 and p = 0.40
n*p = 0.4*25 = 10 and n*(1-p) = 0.6*25 = 15
As n*p and n*(1-p) both are greater than 5 , we have to use normal approximation to binomial distribution.
mean ( µ ) = n*p = 10 and standard deviation (σ) = √(n*p*(1-p) = 2.4495
We are asked to find P( x > 6 )
We have to use continuity correction by adding 0.5 to 6
P( x ≥ 6.5 )
=
= P( z ≥ -1.43 )
= 1 - P( z < -1.43 )
= 1 - 0.0764
= 0.9236
Probability that more than 6 will have tattoos is 0.9236
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