Question 619302
X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
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The measuring stick you have to use to find probabilities 
is the z-chart or technology that you have available.
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(A) P(x < 77.0)
z(77) = (77-80)/3.5 = -3/3.5 = -0.8571
That simply means 77 is 0.8571 standard deviations below the mean.
Now use your z-chart to find the probability to the left of -0.8571
Ans: normalcdf(-100,-0.8571) = 0.1957
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(B) P(75.0 < x < 85.0)
z(75) = (75-80)/3.5 = -1.4286
z(85) = (85-80)/3.5 = +1.4286
P(75<x<85) = P(-1.4286 < z < +1.4286) = normalcdf(-1.4286,+1.4286) = 0.8469
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(C) P(x > 85.0)= P(z > 1.4286) = normalcdf(1.4286,100) = 0.0766
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Cheers,
Stan H.
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