a. The mean of this distribution isb. The standard deviation isc. The probability that the the child will be older than 5 years old?

Answered: a. The mean of this distribution is b.…

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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a. The mean of this distribution is
b. The standard deviation is
c. The probability that the the child will be older than 5 years old?

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Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

The probability density function for uniform distribution with parameters a and b is,

$f (x) = \frac{1}{b - a}; a > 0, b > 0$

The age of children in kindergarten on the first day of school is uniformly distributed between 4.93 and 5.9 years. The random variable x is defined as the age of children in kindergarten on the first day of school

The probability density function is,

$\begin{array}{rcl} f (x) & = & \frac{1}{5.9 - 4.93} \\ = & \frac{1}{0.97} \end{array}$

The mean of the distribution is,

$\begin{array}{rcl} μ & = & \frac{a + b}{2} \\ = & \frac{4.93 + 5.9}{2} \\ = & \frac{10.83}{2} \\ = & 5.415 \end{array}$

Thus, the mean of the distribution is 5.415.

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