In a standard Normal model, what value of z cut off the region described as the lowest 1.5%?

To find the value of z that cuts off the lowest 1.5% in a standard Normal model, you need to determine the z-score that corresponds to the cumulative probability of 0.015.

Step 1: Identify the tail area: In this case, we want the lowest 1.5%, which means we are interested in the left tail of the distribution.

Step 2: Find the z-score: To find the z-score corresponding to the cumulative probability of 0.015 in the left tail, you can use a standard Normal distribution table or a calculator.

Using a standard Normal distribution table, locate the cumulative probability closest to 0.015. The closest value in the table is 0.0158, which corresponds to a z-score of approximately -2.17.

Therefore, the value of z that cuts off the region described as the lowest 1.5% is approximately -2.17.

To determine the value of z that cuts off the lowest 1.5% in a standard normal distribution, you can follow these steps:

1. Start by understanding the standard normal distribution: The standard normal distribution is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. It is also known as the Z-distribution.

2. Find the cumulative probability: The cumulative probability represents the area under the standard normal curve up to a given value of z. In this case, you need to find the cumulative probability for the lowest 1.5%.

3. Determine the z-score: The z-score is a measure of how many standard deviations an observation or value is from the mean of a distribution. It defines the location of a particular value within the distribution.

4. Use a statistical table or calculator: To find the z-value that corresponds to a given percentile, you can use a standard normal distribution table or an online calculator. These tools provide the z-scores for specific percentiles.

In this case, you want to find the z-value that corresponds to the lowest 1.5% in the standard normal distribution. This means you need to find the cumulative probability for this percentile.

Using a standard normal distribution table or an online calculator, you can determine that the cumulative probability for the lowest 1.5% is approximately 0.015.

To find the z-value corresponding to this probability, you need to find the value of z such that P(Z < z) = 0.015. This means you want to find the z-value that gives you a cumulative probability of 0.015.

By referring to a standard normal distribution table or using an online calculator, you can find that the z-value that corresponds to a cumulative probability of 0.015 is approximately -2.17.

Therefore, the value of z that cuts off the region described as the lowest 1.5% in a standard normal distribution is approximately -2.17.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score related to that proportion.