Question 129826: Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that x has an approximately normal distribution with mean μ = 6.8 hours and standard deviation σ = 2.1 hours.
Convert each of the following x intervals to standardized z intervals:
a) x ≤ 7.5
b) 5 ≤ x ≤ 8
c) x ≥ 4
Convert each of the following z intervals to raw score x intervals:
d) z ≥ -2
e) 0 ≤ z ≤ 2
f) z ≤ 3
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let x be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that x has an approximately normal distribution with mean μ = 6.8 hours and standard deviation σ = 2.1 hours.
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Comment:
Convert each of the following x intervals to standardized z intervals:
Comment: For each of these problems you have to find the z-value of the
given x-value. Then find the probility z satisfies the corresponding
inequality. I'll work the 1st one:
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a) x ≤ 7.5
z(7.5) = (7.5-6.8)/2.1 = 0.3333333...
P(z<=7.7) = P(z<=0.333333333) = 0.6306
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b) 5 ≤ x ≤ 8
c) x ≥ 4
Convert each of the following z intervals to raw score x intervals:
Use the same transformation formula but solve for "x":
I'll work the 1st one.
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d) z ≥ -2
z = (x-mu)/sigma
So, x = z*sigma + mu
x = -2*2.1+6.8
x = 2.6
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P(z>=-2) = P(x >= 2.6)
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e) 0 ≤ z ≤ 2
f) z ≤ 3
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Cheers,
Stan H.
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