SOLUTION: The lengths of a certain type of chain are approximately Normally distributed with a mean of 2.2 cm and a standard deviation of 0.2 cm. Find the value of z such that P(Z>z)=0.01.

Algebra ->  Probability-and-statistics -> SOLUTION: The lengths of a certain type of chain are approximately Normally distributed with a mean of 2.2 cm and a standard deviation of 0.2 cm. Find the value of z such that P(Z>z)=0.01.      Log On


   

Question 1192846: The lengths of a certain type of chain are approximately Normally distributed with a mean of 2.2 cm and a standard deviation of 0.2 cm.
Find the value of z such that P(Z>z)=0.01.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the area to the right of the critical z-score is .01
the critical z-score is equal to 2.326347877.
the z-score formula is z = (x - m) / s
z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation
formula becomes 2.326347877 = (x - 2.2) / .2
solve for x to get:
x = 2.326347877 * .2 + 2.2 = 2.665269575.
your solution is:
the z-score that has a probability of any other z-score being greater than it is equal to 2.326347877.
the additional information that i provided to you for your information is:
the raw score that has a probability of another raw score being greater than it is equal to 2.665269575.
these can be seen graphically below.

first the z-score:


second the raw score: