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 $11$ minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

Required:

a$.$ What are the values for a and $b$ in minutes?

Note: Do not round your intermediate calculations. Round your answers to $1$ decimal place.

b$-1.$ What is the mean time to resolve the problem?

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.

Mean

b$-2.$ What is the standard deviation of the time?

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.

Standard deviation

c$.$ What percent of the problems take more than $5$ minutes to resolve?

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.

Percent

d$.$ Suppose we wish to find the middle $50\%$ of the problem$-$solving times. What are the end points of these two times?

Note: Do not round your intermediate calculations. Round your answers to $3$ decimal places.