According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 5 women in this age group:
(1) what is the probability that exactly 2 women were never married?
(2) what is the probability that at most 2 were never married?
(3) find the mean, variance and standard deviation for the binomial probability
distribution.
Answers
Answer:
Step-by-step explanation:
This is a case of binomial distribution. The formula used in calculations for binomial probability is:
P = nCr p^r (1-p)^(n-r)
Where,
P = probability
nCr = combinations of r from n possibilities
p = success rate = 40% = 0.40
n = sample size = 5
1st: Let us calculate for nCr for r = 2 to 5. Formula is:
nCr = n! / r! (n-r)!
10C8 = 5! / 2! 2! = 30
10C9 = 5! / 4! = 15
10C10 = 5! / 5! 0! = 1
Calculating for probabilities when r = 3 to 5:
P (r=3) = 45 * 0.4^3 (0.6)^2 = 1.0368
P (r=4) = 10 * 0.4^4 (0.6)^1 = 0.1536
P (r=5) = 1 * 0.4^5 (0.6)^0 = 0.01024
Total probability that at least 3 were married = 1.0368+0.1536+0.01024
Total probability that at least 3 were married = 1.20064
This was a little harder so please mark this answer as "brainliest" (the crown) if you like this answer + explanation! Have a happy Thanksgiving!