A vertical line is drawn through a normal distribution at z = 0.50, and separates the
distribution into two sections. What proportion of the distribution is in the larger section?
a. 0.6915
b. 0.3085
c. 0.1915
d. 0.3830
You don't even need a set of Normal tables to answer this one. Just remember that the total area under the curve is 1; note that you've been asked to find the proportion of the distribution in the larger section, and then look at the four options. How many answers greater than 0.5 are listed?
To determine the proportion of the distribution in the larger section, we need to find the area under the normal curve to the right of z = 0.50.
Using a standard normal distribution table or calculator, we can find this area.
The area to the left of z = 0.50 is 0.6915, which means the area to the right of z = 0.50 is 1 - 0.6915 = 0.3085.
Therefore, the proportion of the distribution in the larger section is 0.3085.
So the correct answer is option b. 0.3085.
To find the proportion of the distribution in the larger section, we need to calculate the area under the normal curve to the right of z = 0.50.
To do this, we use a standard normal distribution table (also known as a Z-table) or a statistical calculator.
Here's how to use a Z-table to find the proportion:
1. Look up the value for z = 0.50 in the Z-table. The Z-table gives you the proportion of the distribution that falls below a given z-value.
The closest value in the Z-table to 0.50 is 0.6915. However, this represents the proportion in the smaller section (to the left of z = 0.50), not the larger section. The Z-table only provides the proportions for the left side of the curve.
2. Subtract the value obtained in step 1 from 1 to get the proportion in the larger section.
1 - 0.6915 = 0.3085
So, the proportion of the distribution in the larger section is 0.3085.
Therefore, the correct answer is b. 0.3085.