SOLUTION: A population of values has a normal distribution with μ=243 and σ=71.9. You intend to draw a random sample of size n=236.
Find the probability that a single randomly s
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Question 1089085: A population of values has a normal distribution with μ=243 and σ=71.9. You intend to draw a random sample of size n=236.
Find the probability that a single randomly selected VALUE is greater than 247.7.
P(X > 247.7) =
Find the probability that a sample of size n=236 is randomly selected with a MEAN greater than 247.7.
P(M > 247.7) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A population of values has a normal distribution with μ=243 and σ=71.9. You intend to draw a random sample of size n=236.
Find the probability that a single randomly selected VALUE is greater than 247.7.
z(247.7) = (247.7-243)/71.9 = 4.4/71.9 = 0.0612
P(X > 247.7) = P(z > 0.0612) = normalcdf(0.0612,100) = 0.4756
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Find the probability that a sample of size n=236 is randomly selected with a MEAN greater than 247.7.
z(247.7) = (247.7-243)/(71.9/sqrt(236)) = 0.4756*sqrt(236) = 7.306
P(x-bar > 247.7) = P(z > 7.306) = normalcdf(7.306,100) = 1.38x10^-13
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Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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Cheers,
Stan H.
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