Answered: Suppose the time of renting a bicycle…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Suppose the time of renting a bicycle for a customer in a bicycle rental shop is normally distributed with mean 200 minutes and standard deviation 100 minutes.

The rental fee of a bicycle is shown in the table.

(i) Find the mean and the standard deviation of the rental fee of a bicycle.
(ii) If the standard deviation of the time of renting a bicycle is reduced to 50 minutes, find

the new mean of the rental fee of a bicycle.

(Give your answers correct to 4 decimal places if necessary.)

The rental fee of a bicycle is shown in the table.
Number of hours occupied
Rental fee
(i)
≤1.5
1.5-4
$20
$30
$50
≥4
Find the mean and the standard deviation of the rental fee of a bicycle.
If the standard deviation of the time of renting a bicycle is reduced to 50 minutes, find
the new mean of the rental fee of a bicycle.
(Give your answers correct to 4 decimal places if necessary.)

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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