Thread: I wanted to know if I did this correctly.

If I messed up somewhere I dont understand where.
Maybe someone can get some help by me posting this problem too.
I just want to know if Im doing it right because there will be questions like it on my quiz next week.

3. Scores on an endurance test for cardiac patients are normally distributed with mean = 200 and standard deviation = 30.

a. What is the probability a patient will score above 206?
z=206-200/30=.2
This means that the area between the mean and the z point is .2
When you look up .2 on the normal dist. chart you get .0793.
Then you take the other half-.5-and then subtract .0793 to get your prob. So .5-.0793=.4207 and the probability that a patient will score above 206 is 42.07%.

b. What percentage of patients score below 155?

Almost the same as before. You take z=155-200/30=-1.5. You look up 1.5 on the normal standard distribution chart and you get .4332. When you subtract .4332 from .5 you get your answer. The probability that patients score below 155 is .0668 or 6.7%

c. What score does a patient at the 25th percentile receive?

Well, first we look up .25 in the normal standard distribution chart and then find the number .2486(the closest to .25) which has a z score of .67.
We also know that 25% will be below the mean so it will be negative.
If were looking for x, we take x=200-.67(30)=179.9
A patient at the 25th percentile will score 179.9 (or rounded to 180) on the test

Originally Posted by jwells1999

If I messed up somewhere I dont understand where.
Maybe someone can get some help by me posting this problem too.
I just want to know if Im doing it right because there will be questions like it on my quiz next week.

3. Scores on an endurance test for cardiac patients are normally distributed with mean = 200 and standard deviation = 30.

a. What is the probability a patient will score above 206?
z=206-200/30=.2
This means that the area between the mean and the z point is .2
When you look up .2 on the normal dist. chart you get .0793.
Then you take the other half-.5-and then subtract .0793 to get your prob. So .5-.0793=.4207 and the probability that a patient will score above 206 is 42.07%. Mr F says: Correct.

b. What percentage of patients score below 155?

Almost the same as before. You take z=155-200/30=-1.5. You look up 1.5 on the normal standard distribution chart and you get .4332. When you subtract .4332 from .5 you get your answer. The probability that patients score below 155 is .0668 or 6.7% Mr F says: Correct.

c. What score does a patient at the 25th percentile receive?

Well, first we look up .25 in the normal standard distribution chart and then find the number .2486(the closest to .25) which has a z score of .67.
We also know that 25% will be below the mean so it will be negative.
If were looking for x, we take x=200-.67(30)=179.9
A patient at the 25th percentile will score 179.9 (or rounded to 180) on the test Mr F says: I get 179.765 which rounds to 179.8. You're close enough I suppose. But maybe you should try getting a more accurate value of the z-score ... perhaps to a third decimal place if possible?

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