Question

A study of college students stated that 25% of all college students have at least 1 tattoo. In a random sample of 80 college students, let x be the number of students who have at least one tattoo. Find the approximate probability that more than 30 of the sampled students had at least 1 tattoo.

A) 0.0034

B) 0.9929

C) 0.4929

C) 0.0071

Answer 1

n = 80

p = 25% = 0.25

normal approximation to binomial distribution assumptions:-

np = 80*0.25 = 20>10

nq= 80*(1-0.25) = 60 >10

so we can say that the sampling distribution follows a normal distribution with,

the approximate probability that more than 30 of the sampled students had at least 1 tattoo be:-

[ continuity correction as i am using continuous distribution to approximate the discrete distribution]

[ from standard normal table]

(A)

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