Question

Asked Nov 10, 2019

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The age of children in kindergarten on the first day of school is uniformly distributed between 4.92 and 5.7 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.

- The mean of this distribution is
- The standard deviation is

Step 1

**Continuous uniform distribution:**

A random variable *X* is said to have the rectangular distribution or the continuous distribution with parameters (*a*, *b*), if *a* and *b* are the minimum and maximum possible values of *X* respectively, such that the probabilities of getting *X* in all equal intervals within (*a*, *b*) are equal. The probability density function (PDF) of the uniformly distributed random variable with parameters (*a*, *b*) is:

Step 2

Let X be the uniformly distributed variable between 4.92 and 5.7.

Denote X as the age of the children in kindergarten.

Thus, the probability density function of X is:

Step 3

1.

*Mean:*

The mean is obtained a...

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