find z such that 97.5% of the standard normal curve lies to the left of z

To find the value of z such that 97.5% of the standard normal curve lies to the left of z, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we search for the closest probability value of 0.975. The table will give us the corresponding z-value.

In this case, the closest probability value in the table is 0.9750, and its corresponding z-value is approximately 1.96. Therefore, 97.5% of the standard normal curve lies to the left of z = 1.96.

Alternatively, using a calculator, we can use the inverse cumulative distribution function (invNorm) or the normal distribution function (norminv) to find the z-value.

Using the invNorm function with a probability of 0.975, the result is approximately 1.96. Therefore, z = 1.96.

To find the value of z such that 97.5% of the standard normal curve lies to the left of z, you can use a standard normal distribution table or a statistical calculator.

Here's how you can use a standard normal distribution table:

1. Look for the value closest to 97.5% in the table. Most standard normal distribution tables provide values for percentages up to 0.5% or even lower. In this case, you will need to find the closest value to 0.975 (which is 97.5% expressed as a decimal).

2. Locate the corresponding z-value in the table. The z-values are usually found in the margins or columns/rows of the table.

For example, assuming you find that the closest value in the table to 0.975 is 0.9750, then the corresponding z-value would be approximately 1.96.

Therefore, z ≈ 1.96 is the value such that 97.5% of the standard normal curve lies to the left of z.

Keep in mind that the values in the standard normal distribution table are usually rounded, so the exact value may vary slightly.

Use that table again.