Normal Distribution and Standard Deviation

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June 20th 2009, 06:14 PM
scarybear12

Normal Distribution and Standard Deviation

This is the question:
Hermione runs a coaching college and gives all her students an exam at the end of the course. from past experience she knows that the results are normally distributed with a mean of 76.5% and standard deviation of 7.5%. the latest course has 2000 students and hermione offers to refund the cost of the course to any student who does not score a certain percentage.
what should this percentage be if hermione is only prepared to refund 3 students?
justify your answer with calculations and include at least ONE diagram in your solution.

kk.. well ive got an answer with not much working and wonder if there is any more and i cannot find a diagram to use. can someone please help??
June 20th 2009, 06:21 PM
The Second Solution

Quote:

Originally Posted by scarybear12

This is the question:
Hermione runs a coaching college and gives all her students an exam at the end of the course. from past experience she knows that the results are normally distributed with a mean of 76.5% and standard deviation of 7.5%. the latest course has 2000 students and hermione offers to refund the cost of the course to any student who does not score a certain percentage.
what should this percentage be if hermione is only prepared to refund 3 students?
justify your answer with calculations and include at least ONE diagram in your solution.

kk.. well ive got an answer with not much working and wonder if there is any more and i cannot find a diagram to use. can someone please help??

You need the value of x* such that Pr(X < x*) = 3/2000. Use tables (or technology) to find the value of z* such that Pr(Z < z*) = 3/2000. Then $Z = \frac{X - \mu}{\sigma} \Rightarrow z* = \frac{x* - 76.5}{7.5}$ . Substitute the value of z* and solve for x*.
June 21st 2009, 03:38 AM
HallsofIvy

Quote:

Originally Posted by scarybear12

This is the question:
Hermione runs a coaching college and gives all her students an exam at the end of the course. from past experience she knows that the results are normally distributed with a mean of 76.5% and standard deviation of 7.5%. the latest course has 2000 students and hermione offers to refund the cost of the course to any student who does not score a certain percentage.
what should this percentage be if hermione is only prepared to refund 3 students?
justify your answer with calculations and include at least ONE diagram in your solution.

kk.. well ive got an answer with not much working and wonder if there is any more and i cannot find a diagram to use. can someone please help??

Great! Don't complain about "not much working". What working did you do and what answer did you get? I think I might include a "normal curve" graph showing the values given.