Customers experiencing technical difficulty with their Internet cable service may call an $800$ number for technical support. It takes the technician between $30$ seconds and $15$ minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

a$.$ What are the values for a and b in minutes? $($Do not round your intermediate calculations. Round your answers to $1$ decimal place.$)$

b$-1.$ What is the mean time to resolve the problem? $($Do not round your intermediate calculations. Round your answer to $2$ decimal places.$)$

b$-2.$ What is the standard deviation of the time? $($Do not round your intermediate calculations. Round your answer to $2$ decimal places.$)$

c$.$ What percent of the problems take more than $5$ minutes to resolve? $($Do not round your intermediate calculations. Round your answer to $2$ decimal places.$)$

d$.$ Suppose we wish to find the middle $50\%$ of the problem$-$solving times. What are the end points of these two times? $($Do not round your intermediate calculations. Round your answers to $3$ decimal places.$)$