Question

The age of children in kindergarten on the first day of school is uniformly distributed between 4.87 and 5.85 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.

**I JUST NEED HELP ON #3 AND #5**

- The mean of this distribution is
- The standard deviation is
**The probability that the the child will be older than 5 years old?**- The probability that the child will be between 5.17 and 5.57 years old is
**If such a child is at the 65th percentile, how old is that child? years old.**

Step 1

A uniform distribution has an equal probability for all the outcomes of the random variable, that is, it has a constant probability. A uniform distribution is defined over the range (*a*, *b*) where *a* is the smallest value and *b* is the largest value of the distribution. The values, (*a, b*) are the parameters of the uniform distribution.

Step 2

(3)

Consider, *X* be the random variable which represents the age of the children in kindergarten on the first day of school is uniformly distributed with parameters *a*= 4.87 and *b=*5.85.

The probability that children will be older than 5 years can be calculated as:

Step 3

(5)

Percentiles of the continuous uniform distribution on the interv...

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