The
confidence interval of the height is ![\boxed{\left( {37.3,41.1} \right)}.](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cleft%28%20%7B37.3%2C41.1%7D%20%5Cright%29%7D.)
Further Explanation:
Given:
The mean height is ![39.2{\text{ inches}}.](https://tex.z-dn.net/?f=39.2%7B%5Ctext%7B%20inches%7D%7D.)
The standard deviation is
Explanation:
The empirical rule is used to check that the given data set is normally distributed.
Empirical rule is defined as follows,
Approximately
data points will lie within the first standard deviation of the mean.
![\boxed{P\left( {\mu - \sigma } \right) = 70\% }](https://tex.z-dn.net/?f=%5Cboxed%7BP%5Cleft%28%20%7B%5Cmu%20%20-%20%5Csigma%20%7D%20%5Cright%29%20%3D%2070%5C%25%20%7D)
Approximately
data points will lie within the two standard deviation of the mean.
![\boxed{P\left( {\mu - 2\sigma } \right) = 95.4\% }](https://tex.z-dn.net/?f=%5Cboxed%7BP%5Cleft%28%20%7B%5Cmu%20%20-%202%5Csigma%20%7D%20%5Cright%29%20%3D%2095.4%5C%25%20%7D)
Approximately
data points will lie within the three standard deviation of the mean.
![\boxed{P\left( {\mu- 3\sigma } \right)= 99.7\% }](https://tex.z-dn.net/?f=%5Cboxed%7BP%5Cleft%28%20%7B%5Cmu-%203%5Csigma%20%7D%20%5Cright%29%3D%2099.7%5C%25%20%7D)
Here,
represents the mean and
represents the standard deviation.
confidence interval of the mean can be obtained by subtracting or adding one times the standard deviation from the mean,
![\begin{aligned}{\text{Interval}} &= \mu \pm \sigma\\&= 39.2 \pm 1.9\\&=\left( {37.3,41.1} \right)\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%7B%5Ctext%7BInterval%7D%7D%20%26%3D%20%5Cmu%20%5Cpm%20%5Csigma%5C%5C%26%3D%2039.2%20%5Cpm%201.9%5C%5C%26%3D%5Cleft%28%20%7B37.3%2C41.1%7D%20%5Cright%29%5C%5C%5Cend%7Baligned%7D)
The
confidence interval of the height is
Learn more:
- Learn more about normal distribution brainly.com/question/12698949
- Learn more about standard normal distribution brainly.com/question/13006989
- Learn more about confidence interval of mean brainly.com/question/12986589
Answer details:
Grade: College
Subject: Statistics
Chapter: Confidence Interval
Keywords: study, companies, design, furniture, elementary school, classrooms, variety, sizes, kids, different ages, height, kindergarten, children, normal model, 39.2 inches, middle , mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.