Question

A population of 100 contains 12 nonconforming items.
a) What is the probability of selecting a random sample of 25 items containing 3 to 5 nonconforming items? Sampling is without replacement.
b) Calculate the parameters mean and variance of the distribution of nonconforming items in samples of 25.
c) Explain on the meaning of the quantities mean and variance in the context of this problem.

Answer 1

did you get this from a test in online school

Answer 2

no actually my teacher gave this question to practice before test.

Answer 3

oh ok :) do you know where to start?

Answer 4

i can't understand the way he explains that's why i posted this question so that i can learn how to do these types of problems

Answer 5

well duh, unfortunately all i can help with is a way to guide you through it because i do not understand this either :/

Answer 6

@BlackLabel you say something or stop veiwing

Answer 7

hahahaah sorry just negotiating a business deal but I can be of assistance

Answer 8

thanks guys for helping me. i really appreciate it

Answer 9

no problem i will help the best i can :)

Answer 10

so do you know how tis problem is supposed to be worked out ?

Answer 11

Ok firstly we need to use the binomial distribution. You familiar with that?

Answer 12

i think
is it that the one with p(xabsolute N,D, n) formula

Answer 13

it think this equation is called hypergeometric distribution

Answer 14

Dinner time ill bbl. Try to get someone else to help u
Ohhh Ya that may be a better option. Ill check back in a half hr

Answer 15

ok

Answer 16

\[P(3\ nonconforming)=\frac{\left(\begin{matrix}12 \\ 3\end{matrix}\right)\left(\begin{matrix}88 \\ 22\end{matrix}\right)}{\left(\begin{matrix}100 \\ 25\end{matrix}\right)}\]

Answer 17

so x is 3 and n is 25 and defectives are 12 right. i did not get 1 thing that in the question it says 3 to 5 nonconforming so we can assume one?

Answer 18

i think i got how to do part a i got the answer 0.2750

Answer 19

The hypergeometric distribution is generated when a sample of size n is taken, without replacement) from a population containing a items of one particular type and b of others. The probability that the sample contains exactly x of the particular type is given by the relevant term in the hypergeometric distribution.
\[p(x)=\frac{\left(\begin{matrix}a \\ x\end{matrix}\right)\left(\begin{matrix}b \\ n-x\end{matrix}\right)}{\left(\begin{matrix}a+b \\ n\end{matrix}\right)}\]

Answer 20

@Gurmeet Good work! Your answer to part a is correct.

Answer 21

great :)

Answer 22

i didn't get it how to do part b and c

Answer 23

could you also help me do these as well?

Answer 24

you explain really good

Answer 25

b. For the hypergeometric distribution:
\[mean=\frac{na}{a+b}\]
\[variance=\frac{nab(a+b-n)}{(a+b)^{2}(a+b-1)}\]

Answer 26

is mean 3

Answer 27

Yes, your result for the mean is correct.

Answer 28

and is the variance 2

Answer 29

Correct! The variance is 2.

Answer 30

yes :)

Answer 31

what does part c means i didn't get it

Answer 32

The sample mean is the most probable number of of nonconforming items in a sample.

The sample variance 2 is a measure of variation and is the square of the standard deviation.
In this case:
\[Sample\ variance,\ s ^{2}=2\]

Answer 33

*number of nonconforming items

Answer 34

ok so basically we are just explaining our solution right ?

Answer 35

Yes, we are explaining what the sample mean and the sample variance actually mean regarding the question.

Answer 36

Out of 10 loaves on a shelf, 4 are three days old. If the store manager selects 5 loaves at random, what is the probability that:
a) one of the loaves is three days old? Answer: 0.2381
b) x of the loaves is three days old? Answer: \[P(x of the loaves) = (4 nCr x) (6 nCr (5-x)) / (10nCr5)\]

Did i do this correctly? i used hypergeometric distrubution to solve it

Answer 37

Yes, your answers to a) and b) are correct.