Respuesta :
Answer:
a) 0.3731
b) 0.9241
c) Mean = 1.9
Standard Deviation = 0.9987
Step-by-step explanation:
We are given the following information:
P(chocolate chip cookie) = 47.5% = 0.475
Then the number of children follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 4
a) x = 2
We have to evaluate:
[tex]P(x =2)\\= \binom{4}{2}(0.475)^2(1-0.475)^{4-2}\\= 0.3731[/tex]
b) x = 1
We have to evaluate
[tex]P(x \geq 1) = 1 - P(x = 0)\\= 1 - \binom{4}{0}(0.475)^0(1-0.475)^{4-0}\\= 1 - 0.0759\\= 0.9241[/tex]
c) Mean and standard deviation of distribution
[tex]\text{Mean} = np = 4\times 0.475 = 1.9\\\text{Standard deviation} = \sqrt{np(1-p)} = \sqrt{4\times 0.475(1-0.475)} = 0.9987[/tex]
