The spread (i.e., standard deviation) of the standard normal curve is _____. (Do not use percentage to format the number provided here.) The area under the standard normal curve that lies to the left of 1.23, as shown in the figure below, is _____. (Please round the result to 5 decimal places.) Area = ? Z -3 -2 -1 0 1 2 3 z = 1.23
Answer (1)
The subject of this question is Statistics, a branch of Mathematics, which involves the study of data, its analysis, interpretation, and presentation. With respect to the question, we are dealing with the standard normal distribution.
The standard normal distribution is a special normal distribution that has a mean of 0 and a standard deviation of 1. It is often used in statistics because it allows for the standardization of any other normal distribution, which makes it easier to analyze data and compare different datasets.
Spread (Standard Deviation) of the Standard Normal Curve:
The standard deviation of the standard normal distribution is 1. In general, the standard deviation is a measure of how spread out the numbers in a dataset are. In the case of the standard normal distribution, because it is standardized, the standard deviation is 1 by definition.
Area Under the Standard Normal Curve to the Left of z = 1.23:
To find this area, we look up the z-score of 1.23 in the standard normal distribution table, or use a calculator or software that can compute cumulative probabilities for a normal distribution.
After looking up this value, you will find that the cumulative probability (area to the left) for z = 1.23 is approximately 0.89065 .
Therefore, the spread of the standard normal curve is 1, and the area under the curve to the left of z = 1.23 is 0.89065, rounded to five decimal places.
