Question

Suppose that in the certain country the proportion of people with red hair is 29%. Find the following probabilities if 37 people are randomly selected from the populattion of this country. Round all probabilities to four decimals.

(a) The probability that exactly 6 of the people have red hair

(b) The probability that at least 6 of the people have red hair

(c) Out of the sample of 37 people, it would be unusual to have more than people with red hair. Express your answer as a whole number.

Answer 1

(a)

Binomial Distribution

n = 37

p = 0.29

q = 1 - p = 0.71

So,

Answer is:

0.0339

(b) P(X6) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

So,

P(X6) = 1 - 0.0234

= 0.9766

So,

Answer is:

0.9766

(c)
For n = 37, p = 0.29, q = 0.71, referring to Cumulative Binomial Distribution Table, we find :

For X = 14, Cumulative Frequency = 0.0689 = 6.89 %

For X = 15, Cumulative Frequency = 0.0432 = 4.32 % < 5%

So,

we conclude:

Out of the sample of 37 people, it would be unusual to have more than 15 people with red hair.

So,

Answer is:

15