find the z-scores for which 92% of the distribution's area lies between -z and z
you can play around with Z stuff at
http://davidmlane.com/hyperstat/z_table.html
It shouldn't take long to answer your question
To find the z-scores for which 92% of the distribution's area lies between -z and z, we need to find the value of z that corresponds to the cumulative probability of 0.92. Here are the steps to find this value:
1. Determine the area in each tail: Since we want the area between -z and z, we need to find the area in each tail. Since the total area under the standard normal distribution curve is 1, the area in each tail will be (1 - 0.92) / 2 = 0.04.
2. Look up the critical value: Using a standard normal distribution table or a calculator, find the z-score corresponding to a cumulative probability of 0.04.
3. Calculate the z-scores: Subtract the negative z-score obtained in step 2 from the positive z-score obtained in step 2. This will give you the range of z-scores for which 92% of the distribution's area lies between -z and z.
Note: The area between -z and z is also known as the confidence interval.
To find the z-scores for which 92% of the distribution's area lies between -z and z, we need to find the z-score values that correspond to the given cumulative probability.
The first step is to find the area to the left of z in the standard normal distribution, which is 0.5 + (92%/2) = 0.96.
Next, we can use a table or a calculator with the standard normal distribution function to find the z-score corresponding to this cumulative probability.
Using a standard normal distribution table, we can find the z-score corresponding to 0.96, which is approximately 1.751.
So, for 92% of the distribution's area to lie between -z and z, the z-score values would be approximately -1.751 and 1.751.