# Thread: Probability distribution of x

1. ## Probability distribution of x

Hi there...

The question is: One of Canada's well-known distance learning institutions published the age profile of its first-time students. A random sample of 33 students has ten students in their thirties, fifteen students, in their forties, five students in their fifties, and three students in their sixties. A student is selected randomly from the sample. Let x be the age of the selected student.

I believe I've solved the first two parts of the question but am confused by the probability distribution of x (I hope I'm correct that it is .30, .45, .15, .09, which add up to a probability of 1). I am to calculate the expected value of x - the mean - and although I arrived at 45 as the mean, I'm not confident I am calculating this correctly as I think I may be confusing the formulas for discrete vs continuous variables.

Any advice would be greatly appreciated...Shannon

2. The expected value formulas for discrete and continuous variables follow the same basic principle:

Summation of [ x * p(x) ]

1.make the midpoint of each category as 34.5, 44.5, 54.5, 64.5
- for example, the midpoint of 30,31,32,33,34,35,36,37,38,39 is 34.5

2.and extend the probabilities by one decimal place.

You'll get an answer of 44.85, which is a bit more precise.

3. That's great, John...thanks so much! I actually had calculated 44.85 but for some reason, decided to round it off (long day, I guess!).

This forum has been a terrific help. While I'm a loooong way from being proficient, I'm feeling a lot less frustration as I continue to learn from this site.

Have a great day...Shannon

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