Normal distribution

  • #1

Homework Statement


Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves:
P(-X<x-5<X) = .99


Homework Equations


I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the calc as well using the standard (x-mean)/stand dev techniques.


The Attempt at a Solution


I have a good understanding of how to work the general problems as this is the last one out of 50 I have solved. The issue is how to start this one? The teacher left a mysterious hint: Distribution?
 

Answers and Replies

  • #2
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6,876

Homework Statement


Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves:
P(-X<x-5<X) = .99
From the probability above, what you want to solve for is X, not x.

Homework Equations


I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the calc as well using the standard (x-mean)/stand dev techniques.


The Attempt at a Solution


I have a good understanding of how to work the general problems as this is the last one out of 50 I have solved. The issue is how to start this one? The teacher left a mysterious hint: Distribution?

You know that your random variable X is n(5, 4). If you let Y = X - 5, how is Y distributed? What would you need to do to get a probability involving Z, the standard normal n(0, 1) random variable? How should your original probability be rewritten so that it involves Z (and from which you can get the values you need from a table or maybe your TI?
 

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