# Thread: I am not sure how to solve for a probability when N is not given (beginner help).

1. ## I am not sure how to solve for a probability when N is not given (beginner help).

I am having the most trouble with part "a)" but I am comparing the two answers so if you feel inclined to discuss part "b)" as well, I would certainly appreciate it!

The problem:
"The average annual age of doctors in a certain hospital is 43.0 years old with a standard deviation of 3.0 years. Assume that the variable is normally distributed.
(a) Find the probability that the age of a randomly selected doctor is less than 42.32 years.
(b) Find the probability that the mean age of a sample of 25 randomly selected doctors is less than 42.32 years."

I know that "normal distribution" entails that mean=median=mode which I'm thinking might help me solve for N but I'm still stumped. Thank you!

2. ## Re: I am not sure how to solve for a probability when N is not given (beginner help).

From your question, I think you can take the supplied values as population parameters.

The "part a" is then a straight forward calculation using a Z-score and a table of values from a standard normal distribution.

3. ## Re: I am not sure how to solve for a probability when N is not given (beginner help).

Hint: Additionally, think of the sample size in part (a) as N = 1 and part (b) N = 25.

4. ## Re: I am not sure how to solve for a probability when N is not given (beginner help).

Oh ok, I get what you mean. So Z= (value-mean)/SD --> Z= (42.32-43.0)/3.0. Then find value on Z-score table to get probability.

5. ## Re: I am not sure how to solve for a probability when N is not given (beginner help).

Originally Posted by annaml
Oh ok, I get what you mean. So Z= (value-mean)/SD --> Z= (42.32-43.0)/3.0. Then find value on Z-score table to get probability.
Well, no...you're not there quite yet: You want Z= (42.32-43.0)/(3.0/Sqrt[1]).....so you can generalize.

6. ## Re: I am not sure how to solve for a probability when N is not given (beginner help).

Ah yes! I see it now, I was looking at an example in the text where they dropped the sqrt(1). Thank you!!

7. ## Re: I am not sure how to solve for a probability when N is not given (beginner help).

Originally Posted by annaml
Ah yes! I see it now, I was looking at an example in the text where they dropped the sqrt(1). Thank you!!
Okee Dokee.

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