Answer:
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
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 :[tex]P(r=3)=^nC_r p^r q ^{n-r}[/tex]
[tex]P(r=3)=^{7}C_{3} (0.15)^3 (1-0.15)^{7-3}\\P(r=3)=\frac{7!}{3!(7-3)!} (0.15)^3 (1-0.15)^{7-3}\\P(r=3)=0.06166[/tex]
Standard deviation =[tex]\sqrt{n \times p \times q}[/tex]
Standard deviation =[tex]\sqrt{7 \times 0.15 \times (1-0.15)}[/tex]
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
The official record of a high school student’s performance is called:
Answer:
A High School Transcript
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:
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 = [tex]\sqrt{np(1-p)}[/tex]
= [tex]\sqrt{7*0.15(0.85)}[/tex]
= [tex]\sqrt{0.8925}[/tex]
= [tex]0.9447[/tex]
