SOLUTION: A mandatory high school test is normally distributed with mean 400 and standard deviation 73. A. Find the probability that a randomly chosen student has a score better than 500?

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Question 464471: A mandatory high school test is normally distributed with mean 400 and standard deviation 73.
A. Find the probability that a randomly chosen student has a score better than 500?
B. Find the probability that a randomly chosen student has a score between 350 and 550?
C. The top 3% of all students are eligible for a scholarship. What is the minimu score needed to be eligible for the scholarship?
Could you please show the exact steps for solving these questions?
Thanks in advance!
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
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.
.
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.
.
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).
.
Ed