SOLUTION: What is the probability that a normal random variable with mean 6 and standard deviation 3 will fall between 5.7 and 7.5?

Algebra ->  Probability-and-statistics -> SOLUTION: What is the probability that a normal random variable with mean 6 and standard deviation 3 will fall between 5.7 and 7.5?       Log On


   

Question 1150804: What is the probability that a normal random variable with mean 6 and
standard deviation 3 will fall between 5.7 and 7.5?
Found 2 solutions by Edwin McCravy, VFBundy:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Get a TI-83 or TI-84 calculator

Press 2ND VARS 1

The lower value is 5.7
The upper value is 7.5
The µ is 6
The σ is 3

Once you have this:

normalcdf(5.7,7.5,6,3)

press ENTER

read 0.231290364 and round to 0.2313

If you must do it the old fashioned way (with a table), you want to know
what decimal fraction the shaded part (between the two z-values for x=5.7
and x=7.5, which we must calculate) is:



We calculate the z-score for the right-most value 7.5:

z=%28x-mu%29%2Fsigma=%287.5-6%29%2F3=0.5

We calculate the z-score for the left-most value 5.7:

z=%28x-mu%29%2Fsigma=%285.7-6%29%2F3=-0.1

If your table is the newer kind with negative z-values, 
look up z=0.50 in the z-column and the 0 column should read 0.6915.
look up z=-0.10 in the z-column and the 0 column should read 0.4602.
Subtract 0.6915-0.4602 = 0.2313.

If your table is the older kind with no negative z-values, 
look up z=0.50 in the z-column and the 0 column should read 0.1915.
look up z=0.10 in the z-column and the 0 column should read 0.0398.
Add 0.1915+0.0398 = 0.2313.

Sometimes the calculator method will differ in the last decimal place
because the calculator is more modern and accurate than the old-fashioned
table.

Edwin

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Z-score = %287.5+-+6%29%2F3 = 1.5%2F3 = 0.5

Look up 0.5 on a z-table. The result is 0.6915. This means there is a 0.6915 probability the random variable will be below 7.5.


Z-score = %285.7+-+6%29%2F3 = %28-0.3%29%2F3 = -0.1

Look up -0.1 on a z-table. The result is 0.4602. The means there is a 0.4602 probability the random variable will be below 5.7.


The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:

0.6915+-+0.4602 = 0.2313

So, there is a 0.2313 probability the random variable will fall between 7.5 and 5.7.