Questions: The following data represent the flight time (in minutes) of a random sample of six flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. 282, 260, 266, 257, 260, 267 Compute the range and sample standard deviation of flight time. The range of flight time is 25 minutes. The sample standard deviation of flight time is minutes. (Type an integer or decimal rounded to one decimal place as needed.)

Solution Steps

To calculate the range, we identify the maximum ($d_{max}$) and minimum ($d_{min}$) flight times in the dataset.

Given dataset: $D = \{282, 260, 266, 257, 260, 267\}$

$d_{max} = 282$ minutes, $d_{min} = 257$ minutes

The range ($R$) is calculated as $R = d_{max} - d_{min} = 282 - 257 = 25$ minutes.

The mean ($\mu$) of the dataset is calculated as $\mu = \frac{1}{n} \sum_{i=1}^{n} d_i = \frac{1}{6} \times 1592 = 265.333$.

The variance ($s^2$) is calculated using the formula $s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (d_i - \mu)^2$.

Substituting the values, we get $s^2 = \frac{1}{6-1} \times 407.333 = 81.467$.

The sample standard deviation ($s$) is the square root of the variance: $s = \sqrt{s^2} = \sqrt{81.467} = 9$.

Final Answer: