3. \( X \sim N(-1,16) \). Find \( x_{0.6} \)

To find \( x_{0.6} \) for the normal distribution \( X \sim N(-1, 16) \), we first recognize that the mean \( \mu = -1 \) and the standard deviation \( \sigma = \sqrt{16} = 4 \). Next, we need to find the z-score that corresponds to the cumulative probability of 0.6. You can use a standard normal distribution table or calculator for this. The z-score for 0.6 is approximately \( 0.25 \). Now we can convert the z-score back to the original distribution using the formula: \[ x = \mu + z\sigma \] Substituting in the values, we get: \[ x_{0.6} = -1 + (0.25)(4) = -1 + 1 = 0 \] So, \( x_{0.6} \approx 0 \).