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

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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.

  1. The mean of this distribution is 
  2. The standard deviation is 
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Expert Answer

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:

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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:

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1 4.92x5.7 f(x)=5.7-4.92 |0, otherwise 1.28, 4.92 x5.7 0, otherwise f(x)

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Step 3

1.

Mean:

The mean is obtained a...

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