Final answer:
To determine the area under the standard normal curve to the left of given z-scores, the areas are typically found using a z-table or a statistical software. In this case, we need to find the areas for z-scores -1.66, -0.03, -0.26, and 1.08 respectively.
Step-by-step explanation:
The question requires us to calculate the area under the standard normal curve to the left of different z-scores. To do so, we'll reference a z-table, which provides the areas to the left of various z-scores.
- For part (a), the area to the left of Z=-1.66 would need to be looked up in a z-table or calculated using a software or calculator that has the standard normal distribution function.
- For parts (b), (c), and (d), similar processes would be followed for the respective z-scores of Z=-0.03, Z=-0.26, and Z=1.08.
- The area to the left for a specific z-score provides the cumulative probability up to that point on the curve.
In the question's example, the z-table shows the area to the left of z= -0.40 as 0.3446, and the area to the left of z= 1.5 as 0.9332. The difference, 0.5886, is the area between the two z-scores.