Question

A city of Punjab has a 15 percent chance of wet weather on any given day. What is the probability that it will take a week for it three wet weather on

3 separate days? Also find its Standard Deviation

Answer 1

a. 0.06166

b. 0.9447

Explanation:

15 percent is the probability it will rain on any given day. P = 0.15

lets define x as the number of days it will rain in one week.

this solution will follow a binomial distribution.

p(X=x) = nCxP^x(1-p)^x

n = 7

x = 3

1-p = 0.85

p =0.15

inserting these values into the formula

p(X=3)=7C3(0.15)^3(0.85)^4

= 7!/4!3! × 0.003375 × 0.5220

= 35 × 0.003375 × 0.5220

= 0.06166

sd = √np(1-p)

= √7 × 0.15(0.85)

= 0.9447