Question: sampling distribution problem- need help?
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Answer #1:
The Binomial distribution has the probabilityfunction P(x=r)= nCr p^r (1-p)^(n-r)
r=0,1,2,.....,n
where nCr = n! / r! (n-r)!
n=28 (number of people chosen)
p= 0.62 (probability that a person is male)
r=12
A) P(x=12) = 28C12 (0.62)^12 (0.38)^16 = 0.018553
B) This is a geometric distribution problem.
The first 6 calls were men and the 7th call is a woman.
= (0.62)^6 (0.38) = 0.018176
Answer #2:
A - Use the Probability Distribution of a Binomial Random Variable.Use the following formula: P(X = x) = C(n,x) p^x * q^(n-x)
where
n = number of trials
p = probability of success
q = probability of failure = 1-p
In this case n = 28, p = 0.62, q = 0.38, x = 12, therefore, plugging this into the equation we get:
P(X = 12) = C(28,12) * (0.62)^12 * (0.38)^(16)
Your calculator should have a function to calculate combinations, or you can use the following formula: C(n,x) = n! / x! (n-x)!
B - Use the Geometric distribution. This question implies that the first 6 calls are men, and the 7th call is a woman.
Use the following formula: P(X = x) = (1-p)^(x-1) * p
where
p = probability of success
In this case p = 0.38 and x=7, therefore we get:
P(X = 7) = (0.62)^6 * (0.38)
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