Let Z be the standard normal variable with μ = 26 and σ = 3.2. Find the value of P(24 < X < 34).
You can play around with Z table stuff at
davidmlane.com/hyperstat/z_table.html
When I subtract 24-26 and divide it by 3.2 I get -0.625 which is not on the table.
you evidently do not know how to use the Z table. In the first place, you would subtract 24 from 26. But that is no use, since 2/σ just tells you how many σ you are from the mean.
This web site allows you to enter values for μ and σ and then specify the area (probability) between 24 and 34.
Now go back there and start playing around.
I did exactly as my instructor taught. The link to the website you sent did not work. Thanks for your time.
you need to find P(X<34) and P(X<24)
Then subtract to find P(24<X<34)
The link does work. I use it all the time. do a google for Z table calculator if you need to.
Believe me that site works :)
To find the value of P(24 < X < 34), where X is a standard normal variable with μ = 26 and σ = 3.2, we need to use the standard normal distribution and convert the values to z-scores.
The z-score formula is:
z = (X - μ) / σ
First, we calculate the z-score for the lower limit of 24:
z1 = (24 - 26) / 3.2 = -0.625
Next, we calculate the z-score for the upper limit of 34:
z2 = (34 - 26) / 3.2 = 2.5
Now, we can find the probability using the z-table or a calculator.
Using a z-table:
P(24 < X < 34) = P(z1 < Z < z2)
To use the z-table, we look up the cumulative probabilities for each z-score and find the difference.
P(24 < X < 34) = P(Z < z2) - P(Z < z1)
From the z-table, we find the following probabilities:
P(Z < -0.625) = 0.26598553 (approximately)
P(Z < 2.5) = 0.99379033 (approximately)
Therefore, P(24 < X < 34) = 0.99379033 - 0.26598553 = 0.7278048 (approximately)
So, the value of P(24 < X < 34) is approximately 0.7278.