Posted by Jean on Sunday, April 13, 2008 at 1:26pm.
Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. Estimate the probability that among 75 randomly selscted students, at least 20 of them score greater that 78.

statistics  MathGuru, Tuesday, April 15, 2008 at 11:26pm
Use zscores.
z = (x  mean)/sd
With your data:
z = (78  68.2)/10.4 = 0.94
.1736 is the probability using a ztable for a single student with a score greater than 78.
Now we can use a normal approximation to the binomial distribution.
mean = np = (75)(.1736) = 13
standard deviation = √np(1p) = √(75)(.1736)(.8264) = 3.28
Again, use zscores.
z = (20  13)/3.28 = 2.13
Use the ztable to find the probability. (Remember the problem says "at least 20" which means 20 or more.)
I hope this will help.