SOLUTION: Let x be a continuous random variable that has a normal distribution with μ=87 and σ=12. Assuming nN≤0.05, find the probability that the sample mean, x¯, for a
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Question 1079088: Let x be a continuous random variable that has a normal distribution with μ=87 and σ=12. Assuming nN≤0.05, find the probability that the sample mean, x¯, for a random sample of 20 taken from this population will be between 83.9 and 91.5.
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
std error=12/sqrt(20)=2.683
z=(83.9-87)/2.683=-1.155
z=(91.5-87)/2.683=+1.677
probability=0.8292
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let x be a continuous random variable that has a normal distribution with μ=87 and σ=12. Assuming nN≤0.05, find the probability that the sample mean, x¯, for a random sample of 20 taken from this population will be between 83.9 and 91.5.
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z(83.9) = (83.9-87)/[12/sqrt(20)] = -1.1553
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z(91.5) = (91.5-87)/[12/sqrt(20)] = 1.6771
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P(83.9<= x-bar <=91.5) = P(-1.1553<= z <= 1.6771) = 0.8293
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Cheers,
Stan H.
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