# Sampling Distribution??

#### StatsNoob

##### New Member
Ok...the question is...

"Records at the College of Engineering show that 62% of all freshman who declare EE (electrical engineering) as their intended major field of study eventually graduate with an EE major. This fall, the College of Engineering has 316 freshmen who have declared a EE major. What is the probability that between 200 and 225 of them (including 200 and 225) will graduate with an EE major?"

The examples I have in my book have a standard deviation known for a problem like this, however there is no standard deviation given. Need some help with this one.

#### JohnM

##### TS Contributor
This deals with proportions (percentages), and the standard error of a proportion is the square root of (p*q/n). Since the sample size is large, the sampling distribution of a proportion can be modeled by the normal distribution.

#### StatsNoob

##### New Member
Ok...so the square root of p*q/n = .027. Now to work the rest is it

P(200 <= p^ <= 225)?

Mean of p^ is .62
n = 316
q = .38

Do I need the continuity correction? .5/316 = .0015

200 - .62/.027 & 225 - .62/.027 ?

This just doesn't seem right. I think I'm missing something or doing something wrong.

#### StatsNoob

##### New Member
Ok...after racking my brain I came up with this....

Mean = np = 195.92
St.Dev. = sqrt of n*p*q = 8.63

P(199.5 <= x <= 225.5)

199.5 - 195.92 / 8.63 = .41

225.5 - 195.92 / 8.63 = 3.42

so P(.41 <= z <= 3.42)
P(.6591 <= z <= .9997) .9997 - .6591 = .3406

Have I done this right???