Statistics Question!?

Question

A study conducted shows that 58% of a school's graduates find a job in their field afer one year. Find the probability that among 8 randomly selected graduates, at least one finds a job within their field?

a) .580
b) .987
c) .999
d) .125

Answer 1

you need to use the binomial distribution to answer tis question:

P=(n!/(r!*(n-r)!))*p^r*q^(n-r)

or u can use a binomial table instead of the formula. Using the formula gives you the exact ptobability, but since the question is not exactly one, but "at least" one graduate. Then you have to calculate the probability of exactly one, plus exactly two, plus exactly three... etc. Or easier, you can subtract from 1, the probability of none finding a job. This is the same as the probability of "at least 1" or the probability of one or more. In this case


p=probability=.58
n=sample=8
r=number of acurrences=0
q=1-p=.42

Prob=1-P(of 0)
P(of 0)=(8!/0!*8!)*p^0*q^8
being
8!=40320
0!*8!=1*8!=40320
0.48^0=1
0.42^8=.0023054

P(of 0)=.42^8=.0096
P=1-P(of 0)=0.999


.999 is the answer

Answer 2

At least one means 1,2,3,4,5,6,7, or 8 of them find a job.
Instead of calculating these 8 probabilities it would be easier to find the probability that none of them find a job and then subtract that from one.
The probability that a person doesn't find a job is 1-.58 = .42
1 - P(none find a job)
= 1 - P(all 8 do not find a job)
= 1 - (.42)^8
= .9990317348
(c)

Answer 3

P-probability is calculated by dividing the number of graduates who find a job by the total number of selected students
therefore:
P=(58% of 8)/8=(8*0.58)/8=0.58 ...which is a)

Answer 4

so out of 8 students 58% should find jobs.

8x.58=4.64 people who found jobs

we need just 1

4.64/8=.58

Answer 5

I think the answer is
1-(.58)^8
or: 1-.012
or .987

Answer 6

8 are picked from how many?

Answer 7

d