An airliner carries
100
passengers and has doors with a height of
74
in. Heights of men are
normally distributed with a
mean of
69.0
in and a standard deviation of
2.8
in. Complete parts (a) through (d).
a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability is
nothing.
(Round to four decimal places as needed.)
b. If half of the
100
passengers are men, find the probability that the mean height of the
50
men is less than
74
in.
The probability is
nothing.
(Round to four decimal places as needed.)
c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?
The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.
The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
d. When considering the comfort and safety of passengers, why are women ignored in this case?
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 + ...
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