Question

suppose that the percentage of smokers at a college is 20. If a sample of size 200 is selected, what is the probability that we observe a) at least 10% smokers b) exactly 20% smokers c) at most 20% smokers

Answer 1

Solution:-

P = 0.20

n = 200

a) The probability that we observe atleast 10% smokers is 0.99996.

x = 0.10 × 200 = 20

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 20) = 0.999955

b) The probability that we observe exactly 20% smokers is 0.0704.

x = 0.20 × 200 = 40

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x = 40) = 0.0704

c) The probability that we observe atmost 20% smokers is 0.5422.

x = 0.20 × 200 = 40

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x < 40) = 0.5422