MATH SOLVE

2 months ago

Q:
# Flight times for commuter planes are normally distributed, with a mean time of 94 minutes and a standard deviation of 7 minutes. Using the empirical rule, approximately what percent of flight times are between 80 and 108 minutes?

Accepted Solution

A:

Answer:The percent of flight times is 95%Step-by-step explanation:* Lets revise the empirical rule- The Empirical Rule states that almost all data lies within 3 standard deviations of the mean for a normal distribution. - The empirical rule shows that# 68% falls within the first standard deviation (µ ± σ)# 95% within the first two standard deviations (µ ± 2σ)# 99.7% within the first three standard deviations (µ ± 3σ).* Lets solve the problem- Flight times for commuter planes are normally distributed, with a mean time of 94 minutes∴ μ = 94- The standard deviation is 7 minutes∴ σ = 7- One standard deviation (µ ± σ):∵ (94 - 7) = 84∵ (94 + 7) = 101- Two standard deviations (µ ± 2σ):∵ (94 - 2×7) = (94 - 14) = 80∵ (94 + 2×7) = (94 + 14) = 108- Three standard deviations (µ ± 3σ): ∵ (94 - 3×7) = (94 - 21) = 73∵ (94 + 3×7) = (94 + 21) = 115∵ The percent of flight times are between 80 and 108 minutes∴ The empirical rule shows that 95% of the distribution lies within two standard deviation in this case, from 80 to 108 minutes* The percent of flight times is 95%