Final answer:
To calculate the mean flight time and the standard deviation of the flight time, convert the given intervals to minutes. Use the formulas μx = (a + b) / 2 for the mean and σx = (b - a) / √12 for the standard deviation. To find the probability that the flight time will be within one standard deviation of the mean, use the z-score formula.
Step-by-step explanation:
To calculate the mean flight time (μx) and the standard deviation (σx) of the flight time, we first need to convert the given intervals to minutes. 2 hours is equal to 120 minutes, and 20 minutes is equal to 20 minutes. So, the flight time is uniformly distributed between 120 minutes and 140 minutes.
(a) To find the mean, we can use the formula μx = (a + b) / 2, where a is the lower limit and b is the upper limit. In this case, μx = (120 + 140) / 2 = 260 / 2 = 130 minutes.
To find the standard deviation, we can use the formula σx = (b - a) / √12, where a is the lower limit and b is the upper limit. In this case, σx = (140 - 120) / √12 ≈ 20 / 3.4641 ≈ 5.7735 minutes.
(b) To find the probability that the flight time will be within one standard deviation of the mean, we can use the z-score formula. The z-score is calculated as (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, the lower limit would be μ - σ = 130 - 5.7735 ≈ 124.2265 minutes, and the upper limit would be μ + σ = 130 + 5.7735 ≈ 135.7735 minutes. Using the z-score table or a calculator, we can find the probability that the flight time will be between these limits.