The amount of time, in minutes, spent by a customer on one visit to a certain shop is modelled by the random variable X ~ N(μ, σ²). In the past, the values of μ and σ were 10.5 and 3.8 respectively. The shop has recently moved to a new location, and the manager hopes that the new value of μ will be greater than 10.5. He takes a random sample of 10 customers and notes the time they each spend in the shop. He then calculates the sample mean ̄x for these 10 times. Using a hypothesis test at the 5% significance level, the manager finds that there is sufficient evidence to conclude that the new value of μ is greater than 10.5. Stating a necessary assumption, find the smallest possible value of ̄x.