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

Answer:

0.06166

sd = 0.9447

Explanation:

probability of having a wet day on any given day at 15 percent = 0.15 is as follows

Lets define X as the number of days that it is going to rain.

we have x binomial (7, 0.15)

probability(x = 3) = (7 3)p³(1-p)⁴

we have 7!/3!4!(0.15)³(0.85)⁴

= (210/6)*0.003375*0.522

= 35*0.003375*0.522

= 0.06166 approximately 0.0617

b standard deviation = $\sqrt{np(1-p)}$

= $\sqrt{7*0.15(0.85)}$

= $\sqrt{0.8925}$

= $0.9447$