SOLUTION: In a sample of 300 students what is the probability of seeing 32% of the students choosing sports when it is known that on an average 25% of the students go for the sports. It is a

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Question 1030196: In a sample of 300 students what is the probability of seeing 32% of the students choosing sports when it is known that on an average 25% of the students go for the sports. It is assumed that selecting the sports is an independent event.
0.99
0
0.001 or 0.002
Not enough information is given
I have used Poisson distribution =POISSON.DIST(96,75,FALSE) which gave me 0.002. Is this correct?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
My scientific calculator is not powerful enough to evaluate %28matrix%282%2C1%2C+300%2C96%29%29%2A0.75%5E204%2A0.25%5E96, which is the true answer.
If you're going to use the Poisson to approximate this, with lambda+=+np+=+300%2A0.25+=+75, you would get
p%2896%29+=+%2875%5E96%2F96%21%29e%5E-75+=+0.002738, to four significant figures.
I tried approximating using the normal distribution using p%280.315+%3C=+r+%3C=+0.325%29+=+p%282.6+%3C=+z+%3C=+3%29, and I got 0.9987-0.9953 = 0.0034, so more or else the real value should be in the close neighborhood.