What Is the Probability of Age-Related Onset for a Disease?

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hello i really have a problem in my statistic class. please help me
i'm begging you, i don't want to fail. please.. please
the problem is...

suppose the ages at time of onset of a certain disease are approximately normally distributed with a mean of 11 years and a standard daviation of 2 years. A child has just come down with the isease. What is the probability that the child is:
a) between the ages of 9.5 and 15.5 years?
b) Over 11 years of age?
c) Under 10?

it's just one problem please solve it for me
please..
shahi
freshmen student

 

[HallsofIvy]

How is our solving this one problem going to help you? It would be much better for you to go to your teacher. The last thing in the world you want to do is to trick your teacher into thinking you know the subject better than you do!
(By the way, this should be posted in the homework section and you should show us what you have tried.)

In this problem, as in any "normal distribution" problem, the first thing you do is find the "standard variable": z= (x- mean)/standard deviation. In this problem you are told that the mean is 11 and the standard deviation is 2:

a) between the ages of 9.5 and 15.6 years"
translates into z= (9.5-11)/2= -0.75 and z= (15.5- 11)/2= 2.25.
Consult a table of the standard normal distribution (There should be one in your text. If not, there is a nice one at http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html ) to find the probability that z is between -0.75 and 2.25.

b) Over 11 years of age?
That's easy! 11 is the mean. What percentage of any normal population is above the mean? (Of course, that translates to z= 0.)

c) Under 10?
This translates to z= (10-11)/2= -0.5. Find the probability that z is less than -0.5.
(Most tables of the standard normal distribution have only positive z, saving space, since the distribution is symmetric. The probability that z< -0.5 is exactly the same as the probability that z> 0.5. To find the probability -0.75< z< 2.25, find the probability that 0< z< 0.75, the probability that 0<z< 2.25 and add.)

 

[tacman]

Hello Shahi,

I understand that you are facing a problem in your statistics class and you are worried about failing. I am here to help you and I will try my best to guide you through this problem.

The problem you have mentioned is related to the normal distribution of ages at the onset of a certain disease. The mean age is 11 years and the standard deviation is 2 years. We need to find the probability of a child falling into different age ranges.

a) To find the probability of a child falling between the ages of 9.5 and 15.5 years, we need to find the area under the normal curve between these two ages. We can use a statistical calculator or a statistical table to find this probability. Using a calculator, we find that the probability is approximately 0.8186 or 81.86%.

b) To find the probability of a child being over 11 years of age, we need to find the area under the normal curve from 11 years to infinity. This probability is 0.5 or 50%. This means that there is a 50% chance that a child will be over 11 years of age at the onset of the disease.

c) To find the probability of a child being under 10 years of age, we need to find the area under the normal curve from negative infinity to 10 years. This probability is also 0.5 or 50%. This means that there is a 50% chance that a child will be under 10 years of age at the onset of the disease.

I hope this helps you understand the problem better and gives you the confidence to solve it on your own. Remember, statistics can be challenging, but with practice and guidance, you can overcome any problem. If you need further help, please don't hesitate to ask your teacher or a tutor for assistance. Good luck!