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

The probability that it will take a week for it three wet weather on 3 separate days is 0.06166 and its standard deviation is 0.9447

Step-by-step explanation:

Probability of wet weather = 0.15

Probability of not being a wet weather = 1-0.15

We are supposed to find probability that it will take a week for it three wet weather on 3 separate days

Total number of days in a week = 7

We will use binomial over here

n = 7

p =probability of failure = 0.15

q = probability of success=1-0.15

r=3

Formula :
`P(r=3)=^nC_r p^r q ^(n-r)`

`P(r=3)=^(7)C_(3) (0.15)^3 (1-0.15)^(7-3)\\P(r=3)=(7!)/(3!(7-3)!) (0.15)^3 (1-0.15)^(7-3)\\P(r=3)=0.06166`

Standard deviation =
`√(n * p * q)`

Standard deviation =
`√(7 * 0.15 * (1-0.15))`

Standard deviation =0.9447

Hence The probability that it will take a week for it three wet weather on 3 separate days is 0.06166 and its standard deviation is 0.9447