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Question

1 out of 10 is likely
Random sample of 600

a. What is the mean and standard deviation of the distribution of the random variable who are likely?
b. If 120 of 600 respondents are likely, what is the probability that 600 were randomly chosen?

Submitted: 488 days ago.

Category: Math

Value: $9

Status: CLOSED

Posted by Ben Brown 488 days ago.

Info Request

Hi, is question b correct?

If 120 of 600 respondents are likely, what is the probability that 600 were randomly chosen?

488 days ago.

Reply

If I report 120 of my 600 respondents said they are likely to do something, what is the probability that I actually surveyed 600 randomly chosen people?

Accepted Answer

Ok so the random variable in question is a binomial distribution with n=600 and p=1/10

a) Therefore

mean = np = 600x1/10 =60

standard deviation = √( np(1-p) ) = √600x1/10x9/10 = √54 =7.35 (to 2dp)

b) We need to make a normal approximation, Y, to the binomial distribution, X,and see how likely you were to get 120 or more respondents. Both the mean (np) and variance ( np(1-p) ) are greater than 5 so an approximate will be ok

P(X≥120) = P(Y>119.5) allowing for continuity error

=P(Z> (119.5-60)/7.35)

=P(Z>8.10)

=0*

*off the Z tables it is so small

Hence the likelihood you actually surveyed 600 and got 120 likely is practically zero given 1 out of 10 is likely.

I hope this helps.

Expert:	Ben Brown
Pos. Feedback:	99.4 %
Accepts:	469
Answered:	11/18/2008

Mathematician

First Class Honours in Mathematics from Oxford University

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