Final answer:
When transaction times are normally distributed with a mean of 10 minutes and a standard deviation of 1 minute, the percentage of customers who will be satisfied with a transaction time of less than 7.5 minutes is less than 2.5%.
Step-by-step explanation:
The question asks to find the percentage of customers who will be satisfied with a transaction time of less than 7.5 minutes when the transaction times are normally distributed with a mean of 10 minutes and a standard deviation of 1 minute. To find this probability, we need to calculate the z-score of 7.5 minutes using the formula z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation. The z-score represents how many standard deviations an element is from the mean. In this case, z = (7.5 - 10) / 1 = -2.5. We then look up the z-score in the standard normal distribution table to find the probability of a customer being satisfied. Since a z-score of -2.5 corresponds to a very small probability (less than 0.5%), we can conclude that the percentage of satisfied customers will be less than 2.5%.