# Math Help - the normal approximation

1. ## the normal approximation

A clothing manufacturer estimates from past quality control inspections that 4.8% of sweatshirts produced are irregular. If an inspector randomly selects 650 sweatshirts, estimate the probability that at least 30 are irregular.

2. Originally Posted by terminator
A clothing manufacturer estimates from past quality control inspections that 4.8% of sweatshirts produced are irregular. If an inspector randomly selects 650 sweatshirts, estimate the probability that at least 30 are irregular.
Where are you stuck in applying the normal approximation to the binomial distribution? Please show some effort.

3. np = 350x0.10 = 35
n(1-p) =350 x 0.90 = =315

np>=5, n(1-p) >=5
Therefore, the approximation is resonably close to a normal distribution because
np <= 5 and n(1-p) >=5
Now I can calculate the standard deviation
mean = np =35
sd= sqr(npq) =5.61
How do I calculate the probability?

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

4. Originally Posted by terminator
np = 350x0.10 = 35
n(1-p) =350 x 0.90 = =315

np>=5, n(1-p) >=5
Therefore, the approximation is resonably close to a normal distribution because
np <= 5 and n(1-p) >=5
Now I can calculate the standard deviation
mean = np =35
sd= sqr(npq) =5.61
How do I calculate the probability?

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
http://courses.wcupa.edu/rbove/Beren...section6_5.pdf

5. Thanks mr.Fantastic - you're a nice man
"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann