Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
You are expected to use a z-score table to find how many standard deviations correspond to having 10% outside the bounds. It is like having 68% within 1σ. The table interpolates.
I'm sorry I looked everywhere and I still cannot find how to calculate with the data provided. I'm new to stats so any help is appreciated, if there is any more information let me know and I could solve it.
- Using the normal distribution and the central limit theorem, it is found that the mean is of 64.2 inches, while the standard deviation is of 2.66 inches.
- By the Empirical Rule, 99.7% of American women aged 20-29 years have heights between 58.88 and 69.52 inches.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
10% are less than 60.8 inches tall, which means that when [tex]X = 60.8[/tex], Z has a p-value of 0.1, so Z = -1.28, then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{60.8 - \mu}{\sigma}[/tex]
[tex]60.8 - \mu = -1.28\sigma[/tex]
[tex]\mu = 60.8 + 1.28\sigma[/tex]
10% are more than 67.6 inches tall, hence, due to the symmetry of the normal distribution, when X = 67.6, Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{67.6 - \mu}{\sigma}[/tex]
[tex]67.6 - \mu = 1.28\sigma[/tex]
[tex]\mu = 67.6 - 1.28\sigma[/tex]
Then, equaling both equations:
[tex]60.8 + 1.28\sigma = 67.6 - 1.28\sigma[/tex]
[tex]2.56\sigma = 6.8[/tex]
[tex]\sigma = \frac{6.8}{2.56}[/tex]
[tex]\sigma = 2.66[/tex]
[tex]\mu = 67.6 - 1.28\sigma = 67.6 - 1.28(2.66) = 64.2[/tex]
The mean is of 64.2 inches, while the standard deviation is of 2.66 inches.
By the Empirical Rule, 99.7% of the measures are within 3 standard deviations of the mean.
64.2 - 2(2.66) = 58.88
64.2 + 2(2.66) = 69.52
By the Empirical Rule, 99.7% of American women aged 20-29 years have heights between 58.88 and 69.52 inches.
A similar problem is given at https://brainly.com/question/24663213
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
