Question 306615
For μ = 60 and σ = 7
1. z score of 78 = (78-60)/8 = 18/8
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2. z score of 45 = (45-60)/8 = -15/8
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3. probability of 59 = 0
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4. probability of 62 = 0
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5. score at z = 1.64 
x = 1.64*8+60 = 75.12
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6. score at z = –1.96
x = -1.96*8+60 = 44.32
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7. percent less than 73
z(73) = (73-60)/8 = 13/8
Percent < 73 = P(z < 13/8) = normalcdf(-100,13/8) = 0.9479
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8. proportion between 45 and 78
z(45) = (45-60)/8 = -15/8
z(78) = (78-60)/8 = 18/8
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P(45 < x < 78) = P(-15/8 < z < 18/8) = 0.9574
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Cheers,
Stan H.
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