1. **Problem Statement:** We want to find how many derma-rollers out of a sample of 250 will last between 1.5 years and 2.5 years, given that the lifetimes are normally distributed with mean $\mu = 2$ years and standard deviation $\sigma = 0.5$ years (6 months).\n\n2. **Formula and Important Rules:** For a normal distribution, the probability that a value lies between two points $a$ and $b$ is given by \n$$P(a < X < b) = P\left(\frac{a - \mu}{\sigma} < Z < \frac{b - \mu}{\sigma}\right)$$\nwhere $Z$ is a standard normal variable with mean 0 and standard deviation 1.\n\n3. **Calculate the Z-scores:**\n- For $a = 1.5$ years: $$Z_a = \frac{1.5 - 2}{0.5} = \frac{-0.5}{0.5} = -1$$\n- For $b = 2.5$ years: $$Z_b = \frac{2.5 - 2}{0.5} = \frac{0.5}{0.5} = 1$$\n\n4. **Find the probabilities from the standard normal distribution:**\n- $P(Z < 1) = 0.8413$ (from Z-tables)\n- $P(Z < -1) = 0.1587$\n\n5. **Calculate the probability between 1.5 and 2.5 years:**\n$$P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826$$\n\n6. **Find the expected number of derma-rollers lasting between 1.5 and 2.5 years:**\n$$250 \times 0.6826 = 170.65 \approx 171$$\n\n**Final Answer:** 171 derma-rollers will last between 1.5 and 2.5 years.\n\nThis corresponds to option B.