Find the z-score such that the area under the standard normal curve to the left is 0.53.
so, do you have a Z table to consult? What did you find?
No, I looked at the chart from another problem and it wasn't the correct answer.
To find the z-score for a given area under the standard normal curve, you can use a standard normal distribution table or a statistical calculator. However, I will walk you through the steps to determine the z-score manually using the properties of the standard normal distribution.
1. Start by drawing a standard normal curve. The total area under the curve is 1, and it is symmetric around the mean.
2. The area to the left of a particular z-score represents the cumulative probability up to that z-score.
3. In this case, you want to find the z-score for which the cumulative probability to the left is 0.53.
4. Since the normal curve is symmetric, you can find the z-score by determining the corresponding area to the right side of the curve. This can be done by subtracting 0.53 from 1:
Area to the right = 1 - 0.53 = 0.47
5. Now, you want to find the z-score associated with an area of 0.47 to the right of it. To do this, you can use a standard normal distribution table or a statistical calculator. Looking up the value of 0.47 in the table will give you the corresponding z-score.
If you use a standard normal distribution table, you can find the closest value to 0.47, which is usually listed in the table as 0.4708. The corresponding z-score is approximately 1.89.
Therefore, the z-score associated with an area of 0.53 to the left under the standard normal curve is approximately -1.89, considering the symmetry.
In that case, play around here:
http://davidmlane.com/hyperstat/z_table.html
You can see how it all works.
It amazes me how students can get online for help, and not use the amazing resources that are available with just a little help from google.