Final answer:
The probability that at least one confidence interval (CI) doesn't cover the true population mean μ is approximately 1 minus 0.9 to the power of the number of CIs.
Step-by-step explanation:
The probability that at least one confidence interval (CI) doesn't cover the true population mean μ is equal to 1 minus the probability that all CIs cover μ. Since the probability of a CI covering μ is approximately 90 percent, the probability that all CIs cover μ is approximately 0.9 to the power of the number of CIs. Therefore, the probability that at least one CI doesn't cover μ is approximately 1 minus 0.9 to the power of the number of CIs.