Question

In a region, 80% of the population have brown eyes. If 15 people are randomly selected, find the probability that at least 13 of them have brown eyes. Is it unusual to randomly select 15 people and find that at least 13 of them have brown eyes? Why or why not? The probability that at least 13 of the 15 people selected have brown eyes is (Round to three decimal places as needed.)

Answer 1

To answer the above question we first find the probability that atleast 13 of the 15 people selected randomly have brown eyes.

This scenario has binomial distribution with p=0.8 , n=15 .

So here n= 15, p=0.8 4 X~B (nip). PCX =>) = (x pa q n-> PIX?13) = 15 (13.00-8743 (0.232 + 15(16 (0.83 14 .231 + - 15 (15 (0.8) 15 (0.200 +0.1319 + 0.03518 = 0.2308 = 0.3998 PCX7, 13) = 0.391

Here probability that atleast 13 out of 15 people have brown eyes is 0.3978 so rounding of it becomes 0.397

An unusual event is an event whose probability of occurrence is less than or equal to 0.05 .

As one can note the probability of atleast 13 out of 15 people selected randomly will have brown eyes is 0.3978 , which is greater than 0.05 , concluding that it is a usual event.

So it is not unusual to find atleast 13 out of 15 people having brown eyes.

So it is usual to select 15 people and find atleast 13 out of them have brown eyes.