# proportions

#### epoor

##### New member
This problem is about the number of sick days employees at a company miss. It has a normal distrubution with a mean of 11 days and standard distrubution of 1 day. The question is, What proportion of the employees are out fewer than 7.5 days? I guess what I am really confuesed on is the difference between proportions and probability and how to slove for proportions.
Thank you for the help.

#### DrMike

##### Full Member
epoor said:
This problem is about the number of sick days employees at a company miss. It has a normal distrubution with a mean of 11 days and standard distrubution of 1 day. The question is, What proportion of the employees are out fewer than 7.5 days? I guess what I am really confuesed on is the difference between proportions and probability and how to slove for proportions.
Thank you for the help.
The short answer : for this question, they are the same. Work out the probability, and say "the proportion is..."

The long answer : if you say an event has a probability p, what you mean is 'if we try the experiment enough times, in the long run, the proportion of times E happens approaches p' - so that the proportion (number of times E happened divided by number of times the experiment was done) is a measurement of an unknown probability. For example, if you toss a coin 100 times, the number of heads might be 56 - the proportion was .56. If you toss it 1000 times, it might be heads 483 times, so the proportion is .483. If you toss it 1000000 times, you might get (say) 500781 heads, so trhe proportion is .500781. As you toss more and more coins, the proportion will (ie, probability theorists expect it will) approach (ie, converge as a limit to) the 'true' probability, 0.5.