If administrators are selected randomly from the​ faculty, what is the approximate probability that the percentage of male administrators will be 60​% or​ more?

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A large community college district has 2000 ​teachers, of whom 50​% are men and 50​% are women. In this​ district, administrators are promoted from among the teachers. There are currently 60 ​administrators, and 60​% of these administrators are men.
 If administrators are selected randomly from the​ faculty, what is the approximate probability that the percentage of male administrators will be 60​% or​ more?

 

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Follow-up Question

Do your answers suggest that it is reasonable to believe the claim that the administrators have been selected randomly from the​ teachers? Let a probability less than 1​% suggest an unreasonable claim.

It is ___ (reasonable or unreasonable?) to believe the claim that the administrators have been selected randomly since the probability that the percentage of male administrators will be 60​% or more is ____ (near 50%, high, not low, low, 0%, or 100%?) there is a ___% chance it would occur ____ ( tommorow, purposefully, twice more or by chance?) 

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Follow-up Question

 If administrators are selected randomly from the​ faculty, what is the approximate probability that the percentage of female administrators will be 40​% or​ less?

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Follow-up Question

If administrators are selected randomly from the​ faculty, what is the approximate probability that the percentage of female administrators will be 40​% or​ less?

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