Answered: Q2 Let random variable XX be the hair…

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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Q2 Let random variable XX be the hair cut time of customer in one hair salon, and XXfollows uniform distribution on interval [10, 30] (in mins).

1 For one randomly selected customer, find the probability that his/her hair cut time is less than 15 mins.

2 Find the mean and variance of XX.

3 For a sample of 36 randomly selected customers, Specify the distribution of the sample mean hair cut time, and find the probability that the sample mean hair cut time is between 18 and 21 mins (inclusive).

4. For 10 randomly selected customers, find the probability that exactly 3 customers whose hair cut time are less than 15 mins.

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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