SOLUTION: I know this a normal distribution problem, but I am really confused since it is essentially asking us to work backwards. since it is giving us the probability and one point which i

Algebra ->  Statistics  -> Density-curves-and-normal-distributions -> SOLUTION: I know this a normal distribution problem, but I am really confused since it is essentially asking us to work backwards. since it is giving us the probability and one point which i      Log On


   

Question 1023198: I know this a normal distribution problem, but I am really confused since it is essentially asking us to work backwards. since it is giving us the probability and one point which is the lower point of 65, and is asking us to solve for the right end point. How would you solve?
The weight of a 5th grader is normally distributed with a mean of 71 pounds and a variance of 88 pounds^2. Let weight, in pounds, be represented by random variable X.
If P(65 < X < x2) = 0.128. Find x2. (carry all your decimal places, till you get your final answer, then round the final answer to 4 decimal places)

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P%2865%3CX%3Cx%5B2%5D%29+=+0.128
<==>
<==> P%28-0.64%3CZ%3C%28x%5B2%5D-71%29%2Fsqrt%2888%29%29+=+0.128
<==>P%28z%3C=%28x%5B2%5D-71%29%2Fsqrt%2888%29%29+-+P%28z%3C=-0.64+%29++=0.128
==> P%28z%3C=%28x%5B2%5D-71%29%2Fsqrt%2888%29%29+-+0.2611++=0.128
==> P%28z+%3C=+%28x%5B2%5D-71%29%2Fsqrt%2888%29%29+=+0.3891
==> +%28x%5B2%5D-71%29%2Fsqrt%2888%29+=-0.28by directly using a standard normal table.
==> x%5B2%5D+=+68.37