Questions: Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. The area of the shaded region is (Round to four decimal places as needed.)

Solution Steps

The problem provides a standard normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1. The shaded region is between z = -0.98 and z = 1.26.

Using the standard normal distribution table or a calculator, find the cumulative probability for z = -0.98. \[ P(Z < -0.98) = 0.1635 \]

Using the standard normal distribution table or a calculator, find the cumulative probability for z = 1.26. \[ P(Z < 1.26) = 0.8962 \]

Subtract the cumulative probability at z = -0.98 from the cumulative probability at z = 1.26. \[ \text{Area} = P(Z < 1.26) - P(Z < -0.98) \] \[ \text{Area} = 0.8962 - 0.1635 \] \[ \text{Area} = 0.7327 \]

Final Answer