Hello, I am trying to make sure that I'm doing this right.
Question: Determine the probability that a randomly drawn respondent has x correctly identified words where x: is greater than or equal to 8.
Given : Mean of 6 and standard deviation of 2.
My work:
I first drew a picture of a normal distribution (straight line at 8 and the mean of 6 at the center. I shaded the line at 8 all the way to the right)I then used the x-mean/standard deviation formula.
8-6/2=1
The z-score is 1.0. So then I looked it up on my normal curve distribution table and found a value of .34. Then added .5 to .34 and got .84. Then 1-.84 and got .16 (.16 standard deviations above the mean). Looked that up on the table for a value of .0636. .0636 is my final answer.
not sure why you "looked up in the table" twice
the .16 that you got from the 1st iteration is the answer
you might want to go over your technique
That is what my ta taught me. I am trying to make sense of my notes because it is confusing me.
This is the best applet that I have found online.
http://davidmlane.com/normal.html
You can enter the mean and sd directly without bothering about z-scores
enter 6 as the mean
enter 2 as the sd
click on above and enter 8, you will get .84129.... directly
If your course requires you to show the z-score calculations etc,
you can still use this app to check your answers.
btw, you can also use the app to reverse the process by clicking on
"Value from an area" and going from there
@Reiny thank you!
It seems like you have made several steps towards finding the probability. However, let's go through the process again to make sure it is done correctly.
To find the probability of a randomly drawn respondent having 8 or more correctly identified words, you can use the normal distribution.
Step 1: Standardize the value using the formula z = (x - mean) / standard deviation.
In this case, you correctly used the formula with x = 8, mean = 6, and standard deviation = 2:
z = (8 - 6) / 2 = 1.
Step 2: Find the cumulative probability using the standard normal distribution table or a calculator.
To find the probability corresponding to a z-score of 1, you need to determine the area under the standard normal curve to the left of 1.
Looking up the z-score of 1.0 in a standard normal distribution table, you will find the corresponding area as 0.8413.
Step 3: Calculate the probability of x being greater than or equal to 8.
Since you want the probability of x being greater than or equal to 8, you need to find the area to the right of 8.
Since the total area under the curve is 1, you can subtract the cumulative probability from 1:
P(X ≥ 8) = 1 - 0.8413 = 0.1587.
Therefore, the probability that a randomly drawn respondent has 8 or more correctly identified words is approximately 0.1587 or 15.87%.
Remember, it's always a good idea to double-check your calculations to ensure accuracy.