the following data represent the flight time (in minutes) of a random sample of six flights from las vegas…

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.270, 260, 266, 257, 260, 267compute the range and sample standard deviation of flight time.the range of flight time is 13 minutes.the sample standard deviation of flight time is □ minutes.(type an integer or decimal rounded to one decimal place as needed.)

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.270, 260, 266, 257, 260, 267compute the range and sample standard deviation of flight time.the range of flight time is 13 minutes.the sample standard deviation of flight time is □ minutes.(type an integer or decimal rounded to one decimal place as needed.)

Answer

Explanation:

Step1: Find sample mean

First, calculate the average of the flight times. $$\bar{x} = \frac{270 + 260 + 266 + 257 + 260 + 267}{6} = \frac{1580}{6} \approx 263.333$$

Step2: Calculate squared deviations

Find each value's squared difference from the mean. $$(270-263.333)^2 \approx 44.444, \ (260-263.333)^2 \approx 11.111, \ (266-263.333)^2 \approx 7.111$$ $$(257-263.333)^2 \approx 40.111, \ (260-263.333)^2 \approx 11.111, \ (267-263.333)^2 \approx 13.444$$

Step3: Sum squared deviations

Add all the squared deviations together. $$44.444 + 11.111 + 7.111 + 40.111 + 11.111 + 13.444 = 127.332$$

Step4: Compute sample variance

Divide the sum by (n-1) (sample size minus 1). $$s^2 = \frac{127.332}{6-1} = \frac{127.332}{5} = 25.4664$$

Step5: Find sample standard deviation

Take the square root of the sample variance, then round to one decimal place. $$s = \sqrt{25.4664} \approx 5.0$$

Answer:

The range of flight time is 13 minutes. The sample standard deviation of flight time is 5.0 minutes.