SOLUTION: Could you please help me to solve this problem? Must show work Football is the most favorite sport to watch on television for 40% of all adults. Use the normal probability distr

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Question 449788: Could you please help me to solve this problem?
Must show work
Football is the most favorite sport to watch on television for 40% of all adults. Use the normal probability distribution to approximate this binomial probability distribution to find the probability that in a random sample of 500 adults, 185 to 195 will say football is their most favorite sport to watch on television.
The binomial P(185 x  195) = _______

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Football is the most favorite sport to watch on television for 40% of all adults. Use the normal probability distribution to approximate this binomial probability distribution to find the probability that in a random sample of 500 adults, 185 to 195 will say football is their most favorite sport to watch on television.
The binomial P(185 x  195) = _______
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Using the normal approximation you want P(184.5<= x <=195.5)
mean = np = 500*0.4 = 200
std = sqrt(npq) = sqrt(200*0.6) = 10.95
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z(184.5) = (184.5-200)/10.95 = -1.4155
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z(195.5) = (195.5-200)/10.95 = -0.4110
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P(185<= x <=195)~ P(-1.4155<= z <=-0.4110) = 0.2621
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Cheers,
Stan H.