Question

Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a normal model with a mean of 39.2 inches and standard deviation of 1.9 inches. In what height interval should the company expect to find the middle 70% of Kindergartners?

Answer 1

The $70\%$ confidence interval of the height is $\boxed{\left( {37.3,41.1} \right)}.$

Further Explanation:

Given:

The mean height is $39.2{\text{ inches}}.$

The standard deviation is $1.9{\text{ inches}}.$

Explanation:

The empirical rule is used to check that the given data set is normally distributed.

Empirical rule is defined as follows,

Approximately $70\%$ data points will lie within the first standard deviation of the mean.

$\boxed{P\left( {\mu - \sigma } \right) = 70\% }$

Approximately $95.4\%$ data points will lie within the two standard deviation of the mean.

$\boxed{P\left( {\mu - 2\sigma } \right) = 95.4\% }$

Approximately $99.7\%$ data points will lie within the three standard deviation of the mean.

$\boxed{P\left( {\mu- 3\sigma } \right)= 99.7\% }$

Here, $\mu$ represents the mean and $\sigma$ represents the standard deviation.

$70\%$ confidence interval of the mean can be obtained by subtracting or adding one times the standard deviation from the mean,

$\begin{aligned}{\text{Interval}} &= \mu \pm \sigma\\&= 39.2 \pm 1.9\\&=\left( {37.3,41.1} \right)\\\end{aligned}$

The $70\%$ confidence interval of the height is $\boxed{\left( {37.3,41.1} \right)}.$

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949
2. Learn more about standard normal distribution brainly.com/question/13006989
3. 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.

Answer 2

Answer:

The height interval is (37.3, 41.1)

Step-by-step explanation: