A study determined that 8 of persons age 65 to 74 have a cer

A study determined that 8% of persons age 65 to 74 have a certain symptom. A group of 19 persons age 65 to 74 are selected at random. Find the probability that at least 2 persons have the symptom. The probability that at least 2 persons age 65 to 74 have the symptom is (Do not round until the final answer. Then round to the nearest thousandth as needed.)

Solution

probability p = 0.08

q = 1-p = 1 -0.08 =0.92

Use binomial probability distribution formula :

nCr(p)^r(q)^n-r ; n= 19

Probability of Atleast 2 with symptom : 1 - ( probability with symptom none + 1 person symptom)

= 1 - ( 19C0(0.92)^19 + 19C1(0.08)(0.92)^18)

= 1 - ( 0.205 + 0.338)

= 0.456