The age of children in kindergarten on the first day of school is uniformly distributed between 4.9 and 5.79 years old.

Question

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 ________
3. The probability that the the child will be older than 5 years old? _______
4. The probability that the child will be between 5.3 and 5.5 years old is ______
5. If such a child is at the 72nd percentile, how old is that child? ______ years old.

Answer 1

Mean = (4.9 + 5.79) / 2 = 5.345

Standard deviation = √ (b-a)^2 / 12

b = 5.79, a = 4.9

You can calculate this

p (child older than 5) = (5.79 - 5) / (5.79 - 4.9)

p (between 5.3 and 5.5) = (5.5 - 5.3) / (5.79 - 4.9)

72nd percentile = 4.9 + 0.72 (5.79 - 4.9)

1.