Find a z value to the right of the mean so that 74.5% of the distribution lies to the left of it.
To find the z value corresponding to a given percentage, we can use a standard normal distribution table or a calculator.
Given that 74.5% of the distribution lies to the left of the desired z value, we need to find the z value that corresponds to a cumulative probability of 0.745.
Using a standard normal distribution table, we can look up the value closest to 0.745. The closest value is 0.7441, which corresponds to a z value of approximately 0.61.
Therefore, the z value to the right of the mean, such that 74.5% of the distribution lies to the left of it, is approximately 0.61.
To find the z-value that corresponds to a given percentage of the distribution, you can use a standard normal distribution table (also known as a z-table).
First, we need to determine the area under the curve to the left of the desired z-value. Since we want 74.5% of the distribution to lie to the left, we subtract this value from 1 to get the area to the right: 1 - 0.745 = 0.255.
Next, we need to find the z-value that corresponds to an area of 0.255 to the right in the standard normal distribution table. The table provides the area to the left of a given z-value, so we look for the closest value to 0.255 in the table.
Upon consulting the table, the closest value is 0.253, which corresponds to a z-value of approximately 0.67. However, since the value we are looking for is to the right of the mean, we take the negative of this z-value: -0.67.
Therefore, a z-value to the right of the mean so that 74.5% of the distribution lies to the left of it is approximately -0.67.