A noodle machine in Spumoni's 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?

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: C

The number of defectives is approximately normal with mean 0.05 * 1900 = 95 and variance 90.25. Hence the probability of observing at least 115 defectives is approximately the probability that a standard normal exceeds (115-95)/9.5 = 2.105 which is approximately equal to 0.01765.