Final answer:
The probability that a randomly selected quartz time piece will have a replacement time less than 14.3 years is approximately 0.0025, or 0.25%.
Step-by-step explanation:
We are given that the replacement times for the quartz time pieces produced by Company XYZ are normally distributed with a mean of 17.4 years and a standard deviation of 1.1 years. We need to find the probability that a randomly selected quartz time piece will have a replacement time less than 14.3 years.
To find this probability, we first need to standardize the value 14.3 years using the formula z = (x - μ) / σ, where z is the standardized value, x is the observed value, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get z = (14.3 - 17.4) / 1.1 = -2.8182.
Next, we use a standard normal distribution table or a calculator to find the cumulative probability for the standardized value z = -2.8182. The probability of a randomly selected quartz time piece having a replacement time less than 14.3 years is approximately 0.0025, or 0.25%.