SOLUTION: x has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities. a. P(x < 67.0) b. P(67.0 < x

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Question 295886: x has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities.
a. P(x < 67.0)
b. P(67.0 < x < 73.0)
c. P (x > 74.0)
Answer by stanbon(75887) (Show Source):
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x has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities.
a. P(x < 67.0)
z(67) = (67-70)/3 = -1
P(x < 67) = P(z < -1) = 0.1587
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b. P(67.0 < x < 73.0)
z(67) = -1
z(73) = (73-70)/3 = 1
P(67 < x < 73) = P(-1 < z < 1)= 0.6827
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c. P (x > 74.0)
z(74) = (74-70)/3 = 4/3
P(x > 74) = P(z > 4/3) = 0.0912
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Cheers,
Stan H.
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SOLUTION: x has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities. a. P(x < 67.0) b. P(67.0 < x < 73.0) c. P (x > 74.0)