Question 1200131
.
The age of children in kindergarten on the first day of school is uniformly distributed 
between 4.98 and 5.87 years old. A first time kindergarten child is selected at random. 
Round answers to 4 decimal places if possible.

(a) The mean of this distribution is ________
(b) The standard deviation is ________
(c) What is the probability that the child will be older than 5.1 years old? ______
(d) The probability that the child will be between 5.18 and 5.58 years old is ______
(e) If such a child is at the 53rd percentile, how old is that child?_________
years old.
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        For full information about uniform continuous distribution on interval  [a,b]

        in clear and compact form see this web-site https://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm



For  (a)  and  (b),  I will use the formulas from there.



<pre>
(a)  Mean = {{{(A+B)/2}}} = {{{(4.98+5.87)/2}}} = use your calculator.



(b)  The standard deviation = {{{sqrt((b-a)^2/12)}}} = {{{sqrt((5.87-4.98)^2/12)}}} = use your calculator.



(c)  The base interval is (5.87-4.98) years.  The working interval (the gap) from 5.1 to 5.87 is (5.87-5.1) years.

     The probability in this part (c) is the ratio P = {{{the_gap/the_base_intrval}}}


         P = {{{the_gap/the_base_intrval}}} = {{{(5.87-5.1)/(5.87-4.98)}}} = use your calculator.



(d)  The base interval is (5.87-4.98) years.  The working interval (the gap) from 5.18 to 5.58 is (5.58-5.18) years.

     The probability in this part (d) is the ratio P = {{{the_gap/the_base_intrval}}}


         P = {{{the_gap/the_base_intrval}}} = {{{(5.58-5.18)/(5.87-4.98)}}} = use your calculator.
</pre>

Having the formulas and explanations &nbsp;(and the referenced web-site), &nbsp;you can do the rest on your own

and to learn the subject, &nbsp;in parallel.



From now, you just learned and are instructed on how the uniform distribution works.