Respuesta :
Answer:
The height interval is (37.3, 41.1)
Step-by-step explanation:
The [tex]70\%[/tex] confidence interval of the height is [tex]\boxed{\left( {37.3,41.1} \right)}.[/tex]
Further Explanation:
Given:
The mean height is [tex]39.2{\text{ inches}}.[/tex]
The standard deviation is [tex]1.9{\text{ inches}}.[/tex]
Explanation:
The empirical rule is used to check that the given data set is normally distributed.
Empirical rule is defined as follows,
Approximately [tex]70\%[/tex] data points will lie within the first standard deviation of the mean.
[tex]\boxed{P\left( {\mu - \sigma } \right) = 70\% }[/tex]
Approximately [tex]95.4\%[/tex] data points will lie within the two standard deviation of the mean.
[tex]\boxed{P\left( {\mu - 2\sigma } \right) = 95.4\% }[/tex]
Approximately [tex]99.7\%[/tex] data points will lie within the three standard deviation of the mean.
[tex]\boxed{P\left( {\mu- 3\sigma } \right)= 99.7\% }[/tex]
Here, [tex]\mu[/tex] represents the mean and [tex]\sigma[/tex] represents the standard deviation.
[tex]70\%[/tex] confidence interval of the mean can be obtained by subtracting or adding one times the standard deviation from the mean,
[tex]\begin{aligned}{\text{Interval}} &= \mu \pm \sigma\\&= 39.2 \pm 1.9\\&=\left( {37.3,41.1} \right)\\\end{aligned}[/tex]
The [tex]70\%[/tex] confidence interval of the height is [tex]\boxed{\left( {37.3,41.1} \right)}.[/tex]
Learn more:
- Learn more about normal distribution https://brainly.com/question/12698949
- Learn more about standard normal distribution https://brainly.com/question/13006989
- Learn more about confidence interval of mean https://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.
