Question

Based on your z-score and the unit normal table, what is the probability AND percent of obtaining a sample mean of 115.2 or larger?

Type probability here to four decimal places:
Type percent here to two decimal places and include the percent sign:

1. Is finding this sample mean a rare or common occurrence?
a. Rare
b. Common

Answer 1

To find the probability of obtaining a sample mean of 115.2 or larger, you need to calculate the z-score using the formula z = (x - μ) / (σ / √n). Then, you can look up the z-score in the z-table to find the probability.

Step-by-step explanation:

To find the probability of obtaining a sample mean of 115.2 or larger, we first need to calculate the z-score for this value. The z-score formula is z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Given the z-score, we can then use the unit normal table (also known as the z-table) to find the probability.

Let's assume we have a z-table that shows the area under the normal curve to the left of z. The z-score corresponding to 115.2 can be calculated as follows:

z = (115.2 - μ) / (σ / √n)

Once we have the z-score, we can look it up in the z-table to find the area under the normal curve to the left of that z-score. This area represents the probability of obtaining a sample mean of 115.2 or smaller. Subsequently, the probability of obtaining a sample mean of 115.2 or larger is equal to 1 minus the probability of obtaining a sample mean of 115.2 or smaller.