Question

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.

Answer 1

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