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?

• 0.01
• 0.0127
• 0.0177
• 0.0215
• 0.0237

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.