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Topic: Help with probability&stat problem
Replies: 47   Last Post: Jun 16, 2007 4:32 AM

 Messages: [ Previous | Next ]
 Jack Tomsky Posts: 1,835 Registered: 12/18/04
Re: Help with probability&stat problem
Posted: Jun 11, 2007 5:05 PM

> I am looking at solving the following problem:
>
> Past records show that at a given college 20% of the
> students who
> began as psychology majors either changed their major
> or dropped out
> the school. An incoming class has 110
> beginning psychology majors. What is the probability
> that as many as
> 30 of these students leave the psychology program?
>
> I think that I can solve it using the normal
> approximation to the
> binomial probability distribution, as follows:
>
> n =110, p = 0.20
> mean = u = np = 110*0.20 = 22
> standard deviation = s.d. = (n*p*q)^.5 =
> (110*.20*.80)^.5 = 4.1952
>
> We want P(x <=30)
>
> When x = 30, z = (x - u)/s.d = (30 - 22)/4.1952 =
> 1.9069
>
> So, we want P(z<=1.9069) = 0.9717
>
> So, the answer is 97.17 percent.
>
> Can you tell me if you see anything wrong with this
> that I solved this problem? Any help is greatly
> appreciated.
>
> Thanks!
>

Let's start off with the professor's interpretation of the problem which is that we are trying to evaluate Prob(X <= 30). Are you allowed to use the binomial distribution to obtain the calculation exactly?

If X is binomial with p = 0.20 and N = 110, then Prob(X <= 30) = 0.9753, which is slightly greater than your normal approximation.

Jack

Date Subject Author
6/11/07 tutorny
6/11/07 briggs@encompasserve.org
6/11/07 tutorny
6/11/07 Randy Poe
6/11/07 tutorny
6/11/07 Bruce Weaver
6/11/07 tutorny
6/11/07 Bruce Weaver
6/11/07 C6L1V@shaw.ca
6/11/07 Randy Poe
6/11/07 tutorny
6/11/07 Nick
6/11/07 Jack Tomsky
6/11/07 Luis A. Afonso
6/11/07 Jack Tomsky
6/11/07 Luis A. Afonso
6/11/07 Jack Tomsky
6/12/07 Luis A. Afonso
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6/12/07 Luis A. Afonso
6/12/07 Jack Tomsky
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6/13/07 Jack Tomsky
6/13/07 Luis A. Afonso
6/13/07 Anon.
6/13/07 Jack Tomsky
6/13/07 Jack Tomsky
6/13/07 Luis A. Afonso
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6/13/07 Anon.
6/13/07 Luis A. Afonso
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6/13/07 Jack Tomsky
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6/13/07 Jack Tomsky
6/13/07 Luis A. Afonso
6/13/07 Jack Tomsky
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6/14/07 Luis A. Afonso
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