Statistics and probability

Question

n a certain locality 1/3 of the locality is known to be using a particular brand of soap. In a survey sample of 10 households were allotted to each surveyor and 1000 surveyor were appointed. How many surveyor will report a) Exactly 3 user, b) Not more than 3 user, c) At least 4 user?

Answer 1

In a sample of 10, p (exactly 3 users) = C (10,3) (1/3)³ (2/3)⁷

So for (a), find this, multiply by 1000 , and round to nearest whole number

(b)

0 users in 10 (2/3)¹⁰

1 user in 10 C (10, 1) (1/3) (2/3)⁹

2 user in 10 C (10,2) (1/3)² (2/3)⁸

3 user in 10 found in (a)

Add these four up, multiply by 1000, round to nearest whole number

(c)

Subtract probability found in (b) from 1

Multiply by 1000

Round to nearest whole number