Question 464471
a)
z=(500-400)/73=1.37
The area below 1.37 under the normal curve is .915 the probability that a randomly chosen student has a score better than 500.
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b)
z=(550-400)/73=2.05
z=(350-400)/73=-.685
The area between 2.05 and -.685 under the normal curve is .733  the probability that a randomly chosen student has a score between 350 and 550.
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c)
The area under the normal curve of .03 on the right is above 1.88
(x-400)/73=1.88
x-400=137.24
x=538 the minimum score needed to be eligible for the scholarship (537 is acceptable).
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Ed