Posted by
**Sue** on
.

Using standard deviation. Normally distributed mean of 0 degrees standard deviation of 1.00 degrees celcius.

1. between 0 and 1.28

2. greater than 0.37

3. less than -0.92

4. between 1.50 and 2.50

5. between -0.90 and 1.95

6. less than 0

I don't know how to solve these problems.

They are asking for the fraction of the distribution that lies within each of the stated intervals. You can solve these with a table lookup of the normal distribution function, which should be explaied in your text, or by using the handy Java computional tool at

http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html

For the first problem, enter 1.00 for the standard deviation, 0 for the mean, and integration limits "start" and "end" of 0 and 1.28, and then hit the "enter " key. I get 39.97% for that one. The last one (6) is 50%, since the distribution curve is symmetic and you are taking the integral under the curve beyond the mean value. For (4), I get 6.06%. When you are only given one limit, such as in problem (3), take a large number like -10 (ten standard deviations) as the lower limit, since you cannot enter minus infinity as a limit.