Dattaprabhakar G. answered • 07/27/14

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Hello Sheily:

It SEEMS that, if X is a value selected at random from a nromal distribution with mean 50 and SD 6, you want Pr [ 44 < X < 50].

Step 1. Note that 44 < X < 50 is the same as 44 - mean < x - mean < 60 - mean, which is the same as

(44-mean)/SD < (X - mean)/SD < (60 - mean)/SD (since SD is positive, the equality signs do not change).

Substituting in the above inequalities mean = 50 and SD = 6, ... you have -1 < z = (x - 50)/ 6 < 0.

Step 2: Go to the web-link http://www.danielsoper.com/statcalc3/calc.aspx?id=2......Enter z_score = -1.0

you will get the area from - infinity to -1 (to the left of -1) as 0.1586. You know that the are to the left of ZERO under a standard normal curve is 0.5 (due to symmetry).

Therefore area under the curve between -1 and 0 is 0.5- 0.1586 is 0.3414, 34.14 %. Done!