Question

In a certain blood test, CSI people know that the mean value of a response to a reagent is 50.0 with a standard deviation of 13.4 and that the response is normally distributed. Then in a population of 500,000 people in which the response is normally distributed, how many people (correct to the nearest hundred) might be expected to show a response level of 36.6 or lower?

Answer 1

Here's the process.
Calculate a z-score for x=36.6
This isn't too tough. You're just trying to figure out how many standard deviation from the mean 36.6 is. Below the mean gives you a negative z-score. Above gives you a positive z-score. The formula is:
z-score = (x - mean)/(standard deviation)
Next, look up the z-score in a z-table and find out what percentage of a population is lower than that z-score.
Lastly, you know you have a total population of 500000, so multiply that population by your percentage to find the most likely number of people.

Give it a try and ask me any questions that come up.

Answer 2

Is it 170,500 ppl?

Answer 3

No. Notice that 36.6 is exactly one SD below the mean.

Answer 4

340,000???

Answer 5

Oh I feel stupid!!

Answer 6

Nop, I can't find it...