can someone please help me? (probability)?

Question

I've been sitting here all night working on these quantative quizzes for my Bio class, and I have two (seemingly simple) questions that I can't figure out!
#1: A survey found that 10% of older Americans have given up driving. If a sample of 1000 Americans is taken, the standard deviation of the sample is ___?

#2: A survey found that 1 in 5 people say that he/she has visited a doctor in any given month. If 10 people are selected at random, what is the probability that exactly 3 visited the doctor last month?

Any help would be GREATLY appreciated!

I've been sitting here all night working on these quantitative quizzes for my Bio class, and I have two (seemingly simple) questions that I can't figure out!
#1: A survey found that 10% of older Americans have given up driving. If a sample of 1000 Americans is taken, the standard deviation of the sample is ___?

#2: A survey found that 1 in 5 people say that he/she has visited a doctor in any given month. If 10 people are selected at random, what is the probability that exactly 3 visited the doctor last month?

Any help would be GREATLY appreciated!

Crap.Didn't mean to post it twice.Sorry guys!

The choices for the 2nd question are:
a) 10
b) 8.42
c) 9.49
d) 5

Ah ****...see, I've been up too late! lol
Those are the choices for the FIRST one, not the second.
Good god...

Answer 1

Both of these questions concern the binomial distribution. The probability that exactly k people in a sample of n people will have some property if the probability of one person having that property is p is given by n!/((n-k)!k!) * p^k * (1-p)^(n-k). The expected value of this distribution is np and the variance is np(1-p). Therefore:

#1: In this case, n=1000, p=.1, so the variance is 1000*.1*(1-.1) = 90. The standard deviation is therefore √90 ≈ 9.49

#2: In this case, we need to compute the probability exactly, which is easy because the numbers involved are small. This is 10!/(7!3!)*(.2)^3*(.8)^7 = 120 * .008 * 0.2097152 = 0.201326592 .

Answer 2

I don't know about #1

For #2, take 0.8^7 (the probability of NOT visiting a doctor in the last month raised to the number of people who wouldn't have visited a doctor in the last month if three people did.)
Take that number and multiply it by 0.2^3. You should have a very small number at this point.

NOW, "ten choose three" equals (10*9*8)/(3*2*1), which equals 120. This is significant because this is the exact number of combinations you can come up with that will get you exactly three people visitng a doctor. The microscopic number is the probability of a specific ONE of those actually happening. So you want to multiply 120 by the small number.

In other words:

120 * (0.8^7) * (0.2^3)

this equals .2013, or 20.13%

Answer 3

2nd question:
yoiu see the the probality of success is (1/5)= 0.2.
hence if X is the random variable denoting that 3 visited the doctor, the using Bernoulli trials we get
P(X) = (10 C 3) * ((0.2)^3) * ((0.8)^7)
=0.12013


1st question
Sorry dude ,
i haven't done probalility standard deviation yet , but in this case i think you straightway apply the formulae which for a random variable X is
sigma(X)= + squareroot(Var(X))
where Var(X) is the variance of X and sigma(X) is the standard deviation of X which i think you should know.

Answer 4

#1 i am not sure
#2 if 1 in 5 ....100%
2 in 10 .....100 %
to get one more in equation will have probability of selecting the required is one fifth
ie. 3 in 10 ........100% divide by 5
3 in 10 ..........20 %

Answer 5

#1the deviation in any poll or survey--is at best plus or minus 3%--people who do polls or surveys are just like bookies(they try to hit in the middle)--it could be between 70 or 130--give me the juice--want to bet? #2bad question--you can't have 1 in 5 and then change to 10--but i came up with 3.333--let me know

Answer 6

Since ANY help would be appreciated, I can solve #2:

Ther are C(10,3) ways of selecting 3 people out of 10. This equals 10!/(7!3!) = 120.

For each combination, multiply probability for each person:
0.2^3*0.8^7

So 120*0.2^3*0.8^7 = about 0.2