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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 = = = use your calculator.
(b) The standard deviation = = = 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 =
P = = = 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 =
P = = = 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.