Question

In a standard Normal​ distribution, if the area to the left of a​ z-score is about 0.5500​,

what is the approximate​ z-score? Draw a sketch of the Normal​ curve, showing the area and​ z-score.

Answer 1

To find the approximate z-score for an area of 0.5500 to the left of the z-score in a standard normal distribution, we can use the z-table and estimate the z-score by finding the closest z-score in the table that has an area less than 0.5500.

Step-by-step explanation:

To find the approximate z-score for an area of 0.5500 to the left of the z-score in a standard normal distribution, we can use the z-table. The z-table shows the area under the normal curve to the left of a given z-score. From the information provided, we can estimate the z-score by finding the closest z-score in the table that has an area less than 0.5500. For example, if the z-score associated with an area of 0.5500 is -0.40 and the z-score associated with an area of 0.5886 is 1.5, then the approximate z-score for an area of 0.5500 is between -0.40 and 1.5.

We can draw a sketch of the normal curve to visualize this. The area to the left of the z-score will be shaded and labeled as 0.5500. The z-score will be indicated on the x-axis.