13 A noodle machine in Spumoniâs spaghetti factory makes about 5 percent defective noodles even when properly adjusted. The noodles are then packed in crates containing 1900 noodles each. A crate is examined and found to contain 115 defective noodles. What is the approximate probability of finding at least this many defective noodles if the machine is properly adjusted?
If 1900 noodles are packed expected number of defective noodles = 0.05 x 1900 = 95 The standard deviation for the number that accept is \(\sqrt{1900*0.05*.95}\)
Thus we want to estimate the probability
\(P(S_{1900} >= 115) = P(S_{1900} >= \frac{115 - 95} {9.5} )\)
\(P(S_{1900} >= 2.105)\)
Using Z table we get the value
0.0176
confirming using R
1 - pnorm(115,95,9.5)## [1] 0.0176342