Respuesta :
Answer: (4Cx) × (0.25^x) × (0.75^4-x), mean =1, variance = 0.75
Step-by-step explanation:
Total bottle of wine = 12
Number of spoilt wine = 3
p(spoilt wine) = 3/12 = 1/4 = 0.25, q = 1 - 0.25 = 0.75.
n = number of bottles selected randomly = 4.
Since n = 4, then the experiment is of a binomial.
The probability mass function for a binomial distribution is given as
p(x=r) = nCr × p^r × q^n-r
The distribution for x is given below as
P(X=x) = (4Cx) × (0.25^x) × (0.75^4-x)
The mean for a binomial probability distribution is given as
Mean = np = 4×0.25 = 1
Variance = npq = 4×0.25×0.75 = 0.75
A probability is a number that reflects the chance that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.
Probability distribution for X is , P(X=3) = 0.012
mean= 1 , variance = 3/4
From question, number of spoiled wine bottle=3
and total number of bottle is 12
So, Probability of success (spoiled wine bottle) p = 3/12 = 1/4
Probability of unsuccessful (non spoiled bottle) q = 1 - 1/4 = 3/4
Since, A sample of four bottles is randomly selected , n = 4
Probability distribution function, P(X) = ⁿCₓ pⁿ q^(n-x)
Where X represents number of bottles of spoiled wine.
So, P(X=3)= ⁴C₃(1/4)^4(3/4)^1
P(X=3)= 4(1/4)^4(3/4)
P(X=3) = 0.012
Mean = np = 4(1/4)=1
Variance = npq = 4 (1/4)(3/4) = 0.75
Learn more:
https://brainly.com/question/17162435
