A regional airline serving Las Vegas has a base airfare rate of $99. In addition, various fees are charged: for checked baggage, refreshments/drinks in-flight, and for making a reservation on its website. These additional charges average $70 per passenger. Suppose a random sample of 59 passengers is taken to determine the total cost of their flight. The population standard deviation of total flight cost is known to be $40. (a) What is the population mean cost per flight in dollars? $  (b) What is the probability the sample mean will be within $10 of the population mean cost per flight? (Round your answer to four decimal places.)   (c) What is the probability the sample mean will be within $5 of the population mean cost per flight? (Round your answer to four decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...