SOLUTION: 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. Roun

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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.

The mean of this distribution is ________
The standard deviation is ________
What is the probability that the child will be older than 5.1 years old? ______
The probability that the child will be between 5.18 and 5.58 years old is ______
If such a child is at the 53rd percentile, how old is that child?_________
years old.
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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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. 


(a)  Mean = %28A%2BB%29%2F2 = %284.98%2B5.87%29%2F2 = use your calculator.



(b)  The standard deviation = sqrt%28%28b-a%29%5E2%2F12%29 = sqrt%28%285.87-4.98%29%5E2%2F12%29 = 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%2Fthe_base_intrval


         P = the_gap%2Fthe_base_intrval = %285.87-5.1%29%2F%285.87-4.98%29 = 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%2Fthe_base_intrval


         P = the_gap%2Fthe_base_intrval = %285.58-5.18%29%2F%285.87-4.98%29 = use your calculator.

Having the formulas and explanations  (and the referenced web-site),  you can do the rest on your own
and to learn the subject,  in parallel.


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