High School

We appreciate your visit to Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 20 kg 1 What percentage. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 20 kg.

1. What percentage of individual adult females have weights between 74 kg and 84 kg? (Round to one decimal place as needed.)

2. If samples of 81 adult females are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are between 74 kg and 84 kg? (Round to one decimal place as needed.)

Answer :

Final answer:

To find the percentage of individual adult females with weights between 74 kg and 84 kg, we calculate the Z scores and refer to a Z-table, resulting in about 40.1%. For sample means, the Z scores change due to a different standard deviation in the sampling distribution and this time it includes nearly 100% of the sample means.

Explanation:

To answer this question, we need to utilize the Z-score formula, which is Z = (X - μ)/σ where X is the weight, μ is the mean, and σ is the standard deviation.

First, to find the percentage of individual adult females with weights between 74 kg and 84 kg, we need to convert the weight to Z scores. So, for 74 kg, Z = (74 - 79)/20 = -0.25 and for 84 kg, Z = (84 - 79)/20 = 0.25. Using a Z-table, we find that these give us about 40.1% of the population.

For the second part of the question, we need to calculate the sampling distribution standard deviation which equals to the standard deviation divided by the square root of the sample size (σ/√n). With n = 81, we have σ/√n = 20/9 ≈ 2.22. The Z scores for 74 kg and 84 kg are now (74-79)/2.22 = -2.25 and (84-79)/2.22 = 2.25 respectively. Using a Z-table for these values will give us a significantly larger percentage, nearly 100%, as per the Central Limit Theorem.

Learn more about Statistics here:

https://brainly.com/question/31538429

#SPJ11

Thanks for taking the time to read Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 20 kg 1 What percentage. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada