1. **State the problem**: We need to find the two z-scores symmetric about 0 that mark the middle shaded region in a standard normal distribution, where the shaded area is 0.48. 2. **Understand the given information**: The standard normal distribution has mean 0 and standard deviation 1. The shaded area in the middle is 0.48, symmetric about 0, so the area in the tails combined is $1 - 0.48 = 0.52$. 3. **Divide the tail area**: Because the distribution and shaded area are symmetric, half of the tail area lies on each side. So each tail area is $\frac{0.52}{2} = 0.26$. 4. **Find the cumulative area up to the left z-score**: The shaded region lies between $-z$ and $z$, so the area to the left of the negative z-score is the tail area, which is 0.26. 5. **Use the standard normal table or inverse CDF function**: We want to find $z$ such that $$ P(Z < -z) = 0.26 $$ Since the standard normal is symmetric, $$ P(Z < z) = 1 - 0.26 = 0.74 $$ Find $z$ where $$ \Phi(z) = 0.74 $$ 6. **Look up or calculate the z-score**: From standard normal tables or using a calculator, $z \approx 0.61$. 7. **Conclusion**: - Negative z-score = $-0.61$ - Positive z-score = $0.61$ These two z-scores bound the middle shaded area of 0.48 symmetric about zero. **Final answer:** $$\boxed{\text{Negative z-score} = -0.61, \quad \text{Positive z-score} = 0.61}$$