Uniform Distribution

Question

The age of children in kindergarten on the first day of school is uniformly distributed between 4.84 and 6 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 
3. The probability that the the child will be older than 5 years old? 
4. The probability that the child will be between 5.04 and 5.24 years old is 
5. If such a child is at the 19th percentile, how old is that child?  years old.

Answer 1

mean is (4.84 + 6)/2

variance is (6 - 4.84 + 2)(6 - 4.84)/12

standard deviation is square root of variance

probability > 5 = (6 - 5)/(6 - 4.84)

probability between 5.04 and 5.24 = (5.24 - 5.04)/(6 - 4.84)

value of 19th percentile:

0.19 = (x - 4.84)/(6 - 4.84)