SOLUTION: Hi - I know this is probably really simple, are I do not know if I am on the right track for this question (probability is just not making any sense to me at all). It is known

Question 880387: Hi - I know this is probably really simple, are I do not know if I am on the right track for this question (probability is just not making any sense to me at all).
It is known that 25% of all staff in a company make use of the free influenza vaccination programme. Answer the following as: The probability is equal to: (Round your probability to 4 decimal places:
Q If 20 people are randomly selected, find the probability that 8 or more people use the vaccine programme.
So if it is known that 25% of staff make use of the programme, then we can say 75% of staff do not. After that I am stuck.
Please help!
Thanks in advance!

Found 2 solutions by ewatrrr, rothauserc:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
p(make use of vaccine) = .25 n = 20
P(x=12) = 20C12(.25)^12(.75)^8 0r binompdf(20, .25, 12)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
This is a sampling distribution of proportion, we know
sample size is 20 and P(probability of taking vaccination) = .25 and Q(probability of not taking vaccination) = .75
mean of p is .25 and standard deviation of p is square root (PQ/ n) where n is the sample size, therefore
standard deviation of p is square root ((.25 * .75)/ 20) = 0.096824584
now 8/20 = .4
calculate the z value = (.4 - .25) / 0.096824584 = 1.549
consult table of z values for probability associated with the z value
therefore P(X<8) is 0.9393
P(X>8) = 1 - P(X<8)
and P(X>8) = 1 - 0.9393 = 0.0607

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