# Normal Distribution and Standard Deviation

• 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?

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?

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?